Make a list of people to invite. Your friends are throwing the party, so they should take care of invitations as long as you provide them the people with their addresses. Target has cute invitations, or if they're wanting to spend more money go to www.tinyprints.com.
Honestly, I'd tell your friends that you're registering at two or three places and that they can put that on your invitation. Not everyone is going to want to buy you diapers, and you're going to want to have all of the things your baby needs instead of struggling to store twenty boxes of size 1 pampers.
As far as locations go, your local church or community center should have a room you can use if there are going to be a lot of people. If not, your friends should host it at their home. Good luck!