If you leave your credit card, a bike shop will let you ride around for about 10-15 mins. However, many will probably rent you a used bike. Shops will rent bikes.
New bikes can be very pricey, but you can find something nice for around $200-$300. it depends on what you want for bells and whistles. They can cost a lot more, but that range will get you something nice.
I think once you try a bunch of bikes, you'll have a better idea of what to look for. The two models to check out would be a hybrid or a comfort.