Can’t speak for LA, but usually you have to be 16+ to enter weight rooms here I think, and a day fee will range from 10 bucks (in my hometown) to 25 (had to pay that in New York once). My advice is to avoid big health clubs when possible, those are the kind of places that will charge you more, make you take a tour of the facilities/sign a waiver, and may not even let you lift at all if you’re not a member.
Try getting a one-month membership to a place like a YMCA. Look for a chain that has franchises all over the country and allows you to use one membership for lots of different gyms.
I’ve got a YMCA card that gets me in lots of regional YMCA’s without paying extra and with minimal extra paperwork.
Plus, a one-month membership will probably end up being cheaper than buying day-passes for three weeks.
Most of the big chains have some sort of free trial membership. Try Ballys Fitness, 24 Hour Fitness, Planet Fitness, Lifetime Fitness, etc. I know Bally’s has a 14 day free trial if you print out the coupon, then you only need to find one other 7 day trial, or just pay for a week.