I live and work in downtown LA and order delivery for dinner on most nights. There are a few good delivery options downtown. Here are my recommendations.
***** My favorites
Cerveteca. Mexicanish. On GrubHub. Good dishes across the board. Lots of healthy options. Delivery is excellent. Seems too good for delivery.
Gingergrass. Vietnamese. Delivers through TryCaviar (great delivery service). Everything is good. I especially like the fresh and fried spring rolls and the shrimp and yam fritters.
Peking Tavern. Delivers through TryCaviar. Good dumplings, meat-filled wraps, and healthy appetizers. Limited menu though.
Azla Ethiopian Vegan. On GrubHub. Good and unique. A refined, healthy take on Ethiopian. Limited menu.
**** I also like...
Mediterranean City Grill. Middle Eastern. On Eat24 and GrubHub. I like the falafel, the many hummus options, and the salads. Healthy and good. Dependable delivery (restaurant is in DTLA).
Tara's Himalayan. On Eat 24and GrubHub. Strong with the Nepalese menu items (e.g., momos, daal that). Less strong with other menu items. Good delivery.
India's Restaurant. On Eat24 and GrubHub. Pretty good Indian food across the board. I think it would be average on the East Coast, but it's above average for LA. Surprisingly good delivery to DTLA given that it's in Silver Lake.
Manas. On Eat24 and GrubHub. Pretty good Indian food. They excel with tandoori items and rice dishes (e.g., biryanis). Good delivery.
Several Thai options (Flavors of Thai / MyThai / Sib Song / Arunee / Tid Lom). On Eat24 and/or GrubHub. I've had good Thai deliveries from all these places. I don't have strong feelings about any of them Tid Lom has by far the most exotic menu, with many interesting Isaan/Lao dishes. Flavors of Thai is the only one of these restaurants that is located DTLA, and it is dependable.
Papa Cristo's. Greek. TryCaviar. The menu is hit and miss, and the quality is variable. My favorite dish by far is the plaki fish (fish baked en paillotte with diced vegetables, olives, and herbs).
Guelaguetza. Delivers at least through LABite and TryCaviar (also maybe on Eat24 and GrubHub). Interesting Oaxacan food.
Pine and Crane. TryCaviar. Pretty good Chinese food but very limited menu.
El Pollo Grande. Eat24 and GrubHub. Good pupusas and other Salvadoran food.
Spitz. On Eat24 and GrubHub. Pretty good doner (I always get the salads). The french fries and fried garbanzo beans are good too.
Papi's Pizza. On Eat24 and GrubHub. Pretty good pizza. My favorite of all the pizza delivery options which isn't saying much.
Master Chef. On Eat24 and GrubHub. Decent Chinese food with some surprising options (abalone and sea cucumber).
1810 Argentinian. On Eat24 and/or GrubHub. Solid Argentinian food.
Spring Street Smokehouse. On Eat24 and/or GrubHub. Decent BBQ (at least BBQ chicken).
*** You Might Also Try...
Panini Cafe. On LABite. Some pretty good stuff. Seems healthy. Bean-y baked falafel turned me off.
Casa Nostra. On LABite. Average Italian. I don't think Italian delivers very well (especially pasta).
Colori Kitchen. Same as above.
Plum Tree Inn. Mostly mediocre Chinese Food, but better than average for Chinese delivery.
Mandarin Chateau. On Eat24 and/or GrubHub. Same as above.
Border Grill. Delivers through LABite. A few good menu items (e.g., mushroom quesadilla). Lots of disappointing dishes at high prices. The flavors are weird and not really Mexican tasting. I'm puzzled as to why this restaurant is on Jonathan Gold's list of 99 essential restaurants.
Wokcano. On Eat24 and/or Grubhub. Like Border Grill except Pan-Asian.
Local Table. On Eat24 and GrubHub. Nothing appeals to me. But at least the menu is interesting and the restaurant seems to try to make quality food.