BB's answer is excellent, and I know this is an older question, but it's a good one for anyone moving into a rental. I would add a couple of things.
Ask about lawn maintenance - may times, owners pay a third party quite a bit of money to come in every week or two to manage lawn care and snow removal (when and where applicable). If you're willing and able to do either or both, you may be able to negotiate a reduction in rent (just be prepared to uphold your end of the bargain!). This is obviously more likely successful on single family dwellings. By the same token, if lawn care isn't your 'thing' be sure it's included in the rent or you'll be upset (and so will your landlord) when the grass is growing or the snow is falling and you don't want to be responsible for taking care of it :)
Next, ask if you're permitted to paint/change light fixtures/insert any other decorating issues here so that you're clear on what is and is not permitted. I like to decorate so it's important I understand where I can insert 'me' into my rental.
Last, I agree with BB - check out your new neighborhood at night, or on a different day than your first visit - my lesson in this is that as I was looking at a home and ready to hand over the down payment, I decided to drive by on a Friday night, and realized I couldn't get down the street, let alone park, because the house was two blocks away from a large local high school...it should have been obvious to me that this would be an issue, but I didn't realize it until I was in the thick of it.