West Hollywood on the Sunset Strip would be a great area for you guys to stay in. Somewhere like the The Standard, Hollywood has a great pool and party vibe, the The Grafton on Sunset or Sunset Tower Hotel are another two with great locations in that area. Unfortunately I can't speak to if they can accommodate a large party.
In that area you'll have Saddle Ranch Chop House for drinking and their mechanical bull (always makes for great stories!), Katana for dinner and celeb spotting, Drybar, West Hollywood for pre-party blow outs, Bootsy Bellows for the quintessential Hollywood party scene and SoulCycle - West Hollywood for sweating it all out the next day. Plus plenty, plenty more in that area!
I think West Hollywood is one of the few areas in LA where you could safely and easily walk to a variety of restaurants and entertainment .
The Hollywood Roosevelt Hotel is a historic property with a beautiful lobby and pool area. Another possibility is downtown at the Biltmore Hotel, it is historic LA with many bars and restaurants. I love the Sunset Strip for its iconic vibe in the Hollywood Hills but you would definitely need a car. Chateau Marmont is a famous celebrity property. If you decide you would like to be at the beach, Santa Monica is very lively, Shutters On the Beach and Hotel Casa Del Mar are both beautiful properties, but expensive.
You have lots of good suggestions here, so enjoy yourselves and make memories of a lifetime.
West Hollywood would be a better neighborhood to stay in than Los Feliz. In W. Ho you would have access to great restaurants, great hotels and I believe there is a trolley on weekend nights to get you around. You could also stay up on the Sunset Strip, you'd have the Mondrian Hotel- Hollywood ,The Standard, Hollywood and Andaz West Hollywood. I am unsure if these can accommodate 7 but the Chateau Marmont or the Hollywood Roosevelt Hotel should. I hope that gets you started!
You need a car to get around in LA, particularly in West Hollywood. If walking is your intent, I would think Santa Monica/Venice Beach. There are a lot of restaurants and shopping and of course the ocean within a very concentrated area. Also, with 7 girls, airbnb? If WeHo, Chateau Marmont, there is the iconic suite on the top floor hanging over Sunset. And the last suite up the hill is all windows looking out over LA, if you can forget the Belushi connection.
If you want to stay in Los Feliz I would try the Dresden Room. It's a vintage restaurant-piano bar that looks totally stuck in time-not all that girly, but fun. I've been to many a bachelorette party there myself. The couple that sings there is called Marty and Elaine and they've been there for 30 years--it's just a fun, kitschy spot that's good for a laugh. The Good Luck Bar in the area is also good although a little hipstery. If you want a more modern, grown up alternative, I'd go with Rockwell Table & Stage.
As far as public transportation, personally I would just spend the money on the cabs. There's not much of a subway system and taking the buses at night can be a little dodgy.