I'm not sure what exactly you are looking for whether it be convenience, price or a particular type of food but you can find everything in DTLA here...
http://www.downtownla.com/
I'm not much of a fan of LA live. It is convenient but most of the stuff there is either way overpriced or stuff you can find other places like Yardhouse, Wolfgang Puck's etc.
Right near Staples is an El Cholo which has pretty good Mexican food although some Mexicans might not agree. Most of us non-Mexicans like it. Good margaritas too.
A place I like to go to that is about 4 or 5 blocks from Staples is called Big Wangs. It is an affordable sports bar with pretty good wings. The Dublin's on the 7th between Fig/Flower is pretty cheap watering hole.
A fancier restaurant I'd recommend is Roy's Hawaiian on Figueroa and 8th (about 3 blocks from Staples).
Bottega Louie is a decent italian restaurant but that is a bit further. If you go there and you like Whisky maybe go across the street the Seven Grand (corner of 7th/Grand) which is a Whisky bar. They have a pretty extensive list of all types of whisky/whiskey.
If you are looking for a trendy bar with a sweet view, there is a new place called Perch up off 5th and Grand. It is pretty cool but the drinks can be expensive ($8 for a beer but they only served Kronenburg and Fischer when I was there).
You options are basically LA Live, El Cholo or Hooters right next to Staples or you got to walk a few blocks or take the Dash for $0.50. The "F" will take you up and down Fig/Flower:
http://www.dtdash.com/
Oh and if you want some cheap mexican food, check out one of these two places:
http://www.yelp.com/biz/dannys-tacos-los-angeles (the first review even mentions post Kings games.. I park right there and have been a few times - this is a truck on the corner of the street, not a restaurant)
http://www.yelp.com/biz/fernandos-taco-inn-los-angeles (this place is at a car wash across the street from LA Live but it is friggin good)
I love this dive bar if that is your sort of thing...
http://www.yelp.com/biz/back-door-pub-at-the-milner-hotel-los-angeles
the Golden Gopher is another place that is a pretty mellow watering hole:
http://www.yelp.com/biz/golden-gopher-los-angeles