I agree with Cheryl O. The baby won't care where she is. But you will care when she gets over stimulated melts down from too many people, too much noise, attention, and possibly an over abundance of frosting, cake and other goodies.
After getting a few 1st birthdays under my belt, I can tell you, you'll WANT to be at home for the party. If she needs a nap, gets messy, or whatever, you'll be able to change her clothes or get to things you may need, and she'll be happy to be close to the things that matter most: mom, and her favorite lovey.
Most kids that age have a capcity of only an hour or two. The adults will be able to go on for hours. Keep it intimate and at home. If it will be too cramped, does your apartment have a party room?
Otherwise, pick a family style restaurant (Perkins is good) near your apartment, get some tables reserved and keep it quick and simple. If people bring presents that are huge (grandparents are often guilty of this! Lol) ask them to bring them to the apartment so you don't have to worry about putting them in your car to get them home.