I think your concerns about the safety after events at Staples Center is totally unfounded. In all the years the Staples Center and L.A. Live complex has been open, I've never heard of a single incident of a person assaulted or mugged leaving an event. Never. Downtown L.A. is one of the safest neighborhoods in the city and crime stats over the years have backed that up. I lived downtown for over a decade and I can have personally walked all over downtown at all hours, with a few exceptions.
Believe me, if it happened, the local media would be delighted and be all over it. A couple of summers back, a fan was brutally assaulted at a Dodgers game in the parking lot in broad daylight. This was a major news story. The issue was really more about stupid ticketing policy of the team (e.g. giving away prime tickets which ended up with unsavory characters) and non-existent security at the stadium. The whole incident was integral to the ownership selling the team as fans stayed away in droves. Staples Center/L.A. Live is big-time corporate America and they know how to run a very safe venue.
The places to avoid downtown or near downtown are:
1) MacArthur Park to the east of the 110 freeway. Plenty of gang activity here after hours.
2) Skid Row, which is about 2 miles to the north-east. Last person who I personally knew who was mugged had it happen here. It was after midnight on the weekend and he was taking money out of an ATM. I assume you're smarter than this.
3) South of the 10 freeway.
What spooks most people about downtown is a mix of:
1) Areas that contrast poorly to the L.A. Live complex because they are old and run-down and don't look like your neighborhood mall. The Fashion District and Latino Broadway are good examples of this. After hours, they tend to look like sets for a zombie movie.
2) Conversely, the Financial District and Bunker Hill which can be eeirly devoid of people in the evening although this is changing markedly.
Select your hotel based upon your itinerary, not a perception about the safety of the areas surrounding the Staples Center. It is perfectly safe. Most hotels are within walking distance. Only if I were staying at the Omni on Bunker Hill or in Little Tokyo would I take a cab.