Fly away is your best option if you don't want to drive. Its super cheap and convenient.
It will take you from your terminal to union station. From there you can hop on the metro (I think it's the blue line, correct me if I'm wrong), it will take you directly to the staples center.
LAX is about 20-25 minutes away from LAX, then again it really depends on the road condition and also how fast/slow you drive
If you go with Fly Away and then the Metro, expect it to be around 1 hour. It will save you lots of money, rather then renting a car, getting insurance, paying for gas and parking (yuck), this whole thing should be no more than $30 round trip, i don't know how much Fly Away costs nowadays, I want to say $5-7? Metro is about $3-5?
In terms of hotels, if you wanna splurge there is the Ritz Carlton and the JW Marriot, literally right next to the staples center. If you wanna save money, there are plenty of motels and hostels nearby, just google them
Correct me if I'm wrong but i think its the blue line, not the red line! Because I usually take the metro from pasadena to the staples center. I take the Gold - Red - Blue (get off on 7th/Pico? I could be wrong it has been a few months since Ive been there
