Shop around. If you are moving to an apartment, you might want to consider renters insurance. If you can get renters insurance and car insurance at the same place, you generally save more money.
I needed Geico awhile back when I had bad credit and I was without insurance for more than a year. It was about the only place that would actually insure me. A year later, I moved to Tennessee Farm Bureau and saved about $300/6 mos. This was in combination with my homeowners insurance.
No reason not to shop around. There are also independant insurance agents around that will run your numbers through every place he can sell your policy. Several friends have used those type services and gotten great deals.
Shop around is the best advice. I never had a claim with Geico, so I can't comment on that. However, everything else with them was good.