New Haven is safe enough. East Rock is probably safer than downtown in terms of crime against indiviuals (like being mugged) but I think there are a higher number of property crimes in East Rock. I don't think it really makes a huge difference where you live but more about where you feel comfortable. I am female, live on the first floor of an apartment and I walk alone at night and I always walk to and from class. I've never had a problem. However, I think the occupy New Haven group in the green makes it safer at night
--I was a lot more leery walking through the green at night before they were all camped out there. That doesn't mean it is a good idea to walk at night but it isn't like it is teeming with crime. I think Columbia, NYU, GWU, BU, Johns Hopkins, etc. are going to have similar crime issues. It is just a bit unusual that a smaller town has crime issues that are similar to that of a city. As long as you are aware of your surroundings, execute good judgment (like I wouldn't walk home after a night going out by myself--I walk home around 7:30 at night) and keep on regular routes, chances are you will be OK. The shuttle service is a nice perk and there is door to door service at 4PM until 7AM or something like that. It takes extra time but when it is raining or snowing, it is nice to have around. You can always bike as well.
I live in East Rock but I'm moving downtown next year because it will be easier to go back and forth to campus when working on my thesis, etc. Also, it is slightly cheaper for larger places if you want to live alone. There is always Harkness, too.