The biggest factor in choosing a place to live is how much it will cost you. Your rent or mortgage payment will likely account for much of your monthly budget.
Besides your rent or mortgage payments, you'll also have to deal with other expenses that you may not have considered. These include utilities, which your university probably handled while you were in school. On your own, you'll have to pay for water, electricity, gas and sewage.
You'll also have to be wary of less obvious expenses, the kind that can sneak up on you after you've signed on the dotted line. For example, some neighborhoods charge for trash pickup, lawn care, parking spots, alarm permits as well as requiring extra city or state taxes. Depending on the development, you may have to pay a homeowners association fee. Renters may have to pay an additional amount each month for maintenance and upkeep of the property.
In addition to these fees, you'll also need to pay for some form of insurance. Many landlords and property rental companies require their tenants to get renter's insurance before they'll lease them an apartment. Buyers are advised to purchase homeowners insurance, and often lenders require proof of it before they'll loan money to purchase a house.
Once you've taken care of your main expenses, then you'll have to budget for your daily cost of living. In college you probably occasionally spent money on food and drinks, but had a meal plan that kept you fed throughout the school year. Now, however, you'll have to pay for all of your groceries and entertainment, including the basics that used to be supplied for you.
All of these expenses may seem overwhelming at first, but if you do a little research, you can find some great tools online that will help you budget for each cost. Kiplinger's website has a good article about the specifics of each of these expenses.