Downtown Cleveland Lunch
I second the rec. for Lola but instead of the burger, highly recommend the house-made bologna sandwich, which comes with pickles and a fried egg on an english muffin. Paired with the famous Lola fries, there is little better than this combo for a Cleveland lunch. But as mrnyc says, Slyman's would definitely be right up there as well.
corned beef is king in the cleve. i suggest you beef it up and get your corned beef sandwich on at SLYMANS.
JUNIPER GRILL near the ballpark is good for breakfast or lunch too, but they close around 2pm.
i have not been since its revamping, but i hear the diner in the west side market is very good these days. you can take the rapid train at tower city or just walk over over there. bonus is if its a market day your mind will be blown by the bounty and the energy of the mighty wsm! after seeing all that ease your senses back to earth with a local brew at GREAT LAKES across the street. heh.
There is a new branch of Number 1 Pho that opened downtown, on East Fourth Street. Though I agree with Stuart that Superior Pho is the better restaurant, I've heard decent things about this place. Also on East Fourth is Zocalo, which is Mexican. Though it started out to horrible reviews, Next Iron Chef contender Aaron Sanchez was brought in to consult, and there have been some positive comments posted around town since that happened.
The best lunch in downtown Cleveland is Lola - Michael Symon's East Fourth Street restaurant. The Lola Burger is excellent, but I'd stick to Beef Cheek Pierogies and Pork Belly myself.
If you are willing to take public transit, the Red Line runs from Tower City Center to West 25th Street, where you can get outstanding Cambodian food at Phnom Penh Restaurant.
Let us know where you went!
Superior Pho has a great banh mi (Vietnamese sandwich). It seems to be no more than 1.6mi from any of the downtown hotels and as little as 1mi from some, so that's walkable for some definitions of "pretty far."
Alternately, are you willing to take public transportation? I played around in Google transit with the routes from three different downtown hotels and the total trip times (including walking) ranged from 12-22min. There were typically 2-3 different options available in the next 20min. For instance, from Marriott - 12min:
Asia Foods has a pretty good banh mi, too. They also have lots of other good food. I didn't check specifically but they're pretty close to Superior Pho so I expect the travel options will be similar.
There may be other options depending on your willingness to take public transit. Also, since you want to walk, the precise location of your hotel and your tolerance for walking may be helpful.