Hi Allie,
I have only been to the Kitsilano neighborhood once so I am not totally sure of what you are looking for as an equivalent. "Pill Hill" is actually the First Hill neighborhood and is called that (not by anyone i know though) because of the many hospitals in the area. Capitol Hill is the next neighborhood over and to the north of First Hill. Capitol Hill is a very young and urban area. It is home to Seattle's gay community as well. Residents of Capitol Hill are mainly in their twenties to early thirties. It is a mix of artists, students, service industry workers and professionals who work downtown. It is also home to a lot of the cities music community. There are many rock clubs, bars, restaurants etc.. There are areas of the hill that are loud, busy, and a little trashy. There are also areas that are very quiet and full of beautiful old bungalow style homes and brick apt buildings. I would suggest the area around 15 th avenue since you have a small baby. You can walk some of Seattle's oldest and most beautiful neighborhoods here. There are a few really good natural grocery stores in the area as well as indie coffee shops and Volunteer Park is here too. If you choose to live somewhere else besides Cap. Hill i would suggest Queen Anne Hill or the Wallingford/ Fremont area. There are a lot of great neighborhoods to choose from in Seattle so drive around before you choose. Good Luck!