That Marriott is on the edge of Downtown Mesa. That's a pleasant, walkable area, although it's not lively after 8 or 9 PM unless there's a special event going on. Some good choices within walking distance of the hotel are the following:
-- Mango's Mexican Cafe. Tacos, Tortsa, Burritos. Order at the counter informality, but good mainstream Arizona Mexican food. No liquor license.
-- Nunthaporn. Thai food. I really like their jungle curry. Beer and wine.
-- Desert Eagle Brewing. Recently established craft brewery. Just starting to dabble in food. Good place for a pint before or after a meal at Mango's or any other place that does not serve alcohol.
-- Blue Adobe Grill. New Mexican food.
For informal lunches or early dinners, you might also try Queen's Pizza, Urban Picnic, or Cucina Di Vita
If you have a rental car or are willing to take the buses along Main Street (either LINK or route 40), a journey 2.5 miles west to Dobson Road is a good idea. On the southeast corner of Dobson & Main, the mostly deserted shopping center is home to Asian Cafe Express, a great hole-in-the-wall Chinese restaurant. On the southwest corner, there's Mekong Plaza, a small mall that focuses on the southeast Asian community. My favorite full service restaurant there is unPhogettable. In the food court, you'll find more specialized purveyors of various regional cuisines: Hue Gourmet (central Vietnam), My Tho (Mekong Delta), and Wholly Grill (Filipino)