Congratulations!
I've read about UChicago's program since I'm a MSW student and located in Illinois; my impression was quite positive.
Warning
I'm a Chicago resident so I'm a little biased, but I'll be as objective as possible.
Academics
Word has it that UChicago's SSA program is quite a cerebral/intellectual atmosphere when compared to other MSW programs. If you're up for that then give a point to UChicago.
Regarding the clinical track, I'd say compare both program's course requirements for each. Here's
UChicago's (course
description) and here's
NYU's. Read each course description for each mandatory track and the clinical electives you'd take at each.
Caveat: Keep in mind that UChicago runs on a quarter system compared to a semester (NYU). This means that you'll be taking more courses compared to a semester, which brings more exams. You'll have the chance to take more clinical courses if that's what you want, but it may also mean less practice with each prevention method. So compare NYU's curriculum for each semester until your internship and how many mandatory clinic courses there are compared to how many elective you can take.
Also note that developing into a competent clinician is achieved through many years of practice once you graduate, but I'm aware that a solid foundation is also needed in order to have some confidence once you get into counseling/therapy. Some MSW programs focus too much on policy/administration in expense to clinical training. Again, make sure you compare what each program offers in what you want for each specialty & demographic.
I'd also compare pass rates first time for the LCSW and see what past students are up to. Contact each department to see if they can put you in contact with an alumnus and current student, this way you can pick their brains. I've done this with my current program and it helped ease some worries while also making me confident I was making the correct choice.
Tuition
You mentioned you had a scholarship to each with UChicago giving you double the money . Compare the difference and if the difference is negligible then factor in personal expenses (see: below). If not, keep in mind that social services usually aren't well paying jobs. An MSW isn't like a prestigious law, business or medical degree where the ROI is a risk but it pays off years later (add in the social *prestige). From what I gather many MSW's aren't the entrepreneur type and don't delve into private practice, so paying off loans must be taken into account if you find yourself filling out the FAFSA for financial aid. I've heard personal stories that people regretted going to Columbia and later facing the reality of paying off 90K loans. You have a scholarship to each, so you're in a better place than they are tuition wise.
Does NYU and UChicago offer assistanships? If they do then that helps lower the cost of tuition.
*It really doesn't matter where you get your MSW, but in terms of pure academic prestige for those that actually know academia, UChicago is hard to beat.
Personal Expenses
Both Chicago and NYU are expensive cities. Chicago is the less expensive of the two. I have a brother currently living in Manhattan and he directly said that he'd live "like a king" on his salary if he were back in Chicago.
Factor in housing cost. Factor in food expenses. Factor in transportation (are you taking a car? how about public transportation?). Which university is closer? If one or the other is close, that would ease the cost of moving.
Simply put, your dollar goes farther in the Midwest.
City
When people complain that they don't want to attend graduate school in a small town I'm always tempted to ask if they attended their undergraduate in a small town with a follow-up question if they didn't mind living in a small town. If they say yes to the first and give a "didn't really mind" to the second then I always point that being in a small town would be the least of their problems. They should be too busy studying and writing research papers to even care that much.
In your case, I go about it differently. I will always say, unless you got some major coin in the bank for housing, pick the less expensive city. Of course, I'm biased since I'm from Chicago, but I'm aware enough that expenses are tight for graduate students and saving any money lessens the financial pain 99.9% of us face once we graduate.
NYU, being in Manhattan, is surrounded by (high) culture and ethnic diversity. It's cosmopolitan to the "T", from Manhattan to certain parts of Northwest Brooklyn. I get the feeling you know this, so I won't dwell on it. Chicago has culture as well, but it's more "pound for pound" - what I mean by this is that the cultural amenities aren't as numerous as it would be in NYC yet it still offers first-rate institutions. Lesser museums, lesser people, lesser restaurants etc. This isn't bad, truly it isn't. What NYC has Chicago can match, for the most part. I'm going to purchase tickets to the Joffrey Ballet to see Christopher Wheeldon's re-imagining of Tchaikovsky's Nutcracker, which will have it's world premiere this December. I usually attend the opera at least once a year, depending on their performance selection, and I will say the Lyric Opera is grand (I take it you'll be full-time, if so, students get a discount that ranges from $20-65 per ticket). Chicago does have its musicals, sometimes a few try-outs come to the city and later transfer to Broadway, but a good majority of the musicals in The Loop are on tour. As for plays, Chicago is internationally known for its stage companies e.g. Steppenwolf, The Lookingglass Theater. Food? I can only see people complaining that there aren't enough options, but I never heard of that all my time here. Though, be aware that Chicago is more of a bar city.
If you want a Times Square feeling, Chicago doesn't really have that unless it's Michigan Ave. during the warmer months. The city's aesthetics are different as well - no Brooklyn or Washington Bridge, though there is Lake Michigan, which is practically a hidden gem for sailing and swimming. If you attend UChicago and stay during the summer you can venture into Michigan and see their own horizons of Lake Michigan - simply whimsical.
If you want professional sports Chicago is the place besides Boston for urban settings.
NYC does beat Chicago in certain areas, like fashion (Fashion Week/Met Gala), Broadway (mostly musicals), tv production and niche museums.
Weather
Both cities aren't paradises. They're not Miami or L.A. weather wise. But, given that, Chicago is the worst of the two. If you don't have
good winter wear you'll need to get them, which also can be expensive (I personally just received my shipping notification for my LL Bean boots).
Transportation
Both cities have the most comprehensive public transportation in the US. Depending on who you talk to about each, it's a love-hate relationship. Mind you, and it's a somewhat funny reality, people who live in NYC tend to not venture out of their boroughs despite how close they are to other major cities along the N-E Corridor and the camping/hiking opportunities found within New York state. It's easier to rent a car in Chicago and go to other places within Illinois. If you want to got to Milwaukee it's just little over an hour away. In my observations students usually stay in the city, whether it be NYC or Chicago.
Safety
This probably the most important section if we exclude tuition. I believe the safety precautions are the same for every urban area: don't travel - alone - in parts that are known to be seedy and sketchy at night, don't walk in dark alleys and don't walk where there is a lack/absence of light (street with no lamps).
I've bet you've heard the national crisis of the homocides that occur in Chicago. They're all true, but the national coverage and commentary on it is wanting. A chunk, like 75% of the city of Chicago is relatively safe. It's certain pockets on the West Side and South Side where the the homocides occur. UChicago is located in Hyde Park on the South Side, but that neighborhood is gentrified and is its own little bubble - both intellectually and in safety. You travel a 10 minutes West and South of Hyde Park you're in another world. NYU is located in Greenwich Village and its surrounding neighborhoods are safe.
Campus
NYU is fully integrated into Manhattan - there really isn't any "official quad" or grounds. NYC is the grounds. Besides a few buildings conglomerated together, NYU lacks in its collegiate atmosphere. UChicago is more of a traditional campus. It's
darn right beautiful at times; the
city isn't too shabby, too.
Conclusion
If price isn't much of factor (tuition, rent, food), and you noted that you want to live in NYC, then pick NYC. If you want more of a traditional campus with an intellectual atmosphere and a short train/bus away to (high) culture then you might want to consider Chicago.
