Here are my faves:
Mirage, on Gulf-to-Bay at Belcher: This Mom and Pop Persian restaurant has a wonderful buffet with veggie and meat offerings. The lunch buffet is a value at 10 bucks. I'm not a big buffet person, but I make an exception here because the food is so fresh and the preparations so good.
Pierogi Grill, on Gulf-to-Bay by Highland: You can order a sampler plate of 12 pierogis for 10 bucks; most other Polish specialties aren't much more than that.
Mi Tierra Colombiana, on Highland south of Gulf-to-Bay: This is another wonderful, unsung Mom and Pop restaurant with stick-to-your-ribs offerings, most of which are under 10 bucks. You typically can't go wrong with their daily specials; I also like their empanadas and pollo a la plancha (grilled chicken breast).
Umbertos, on Patricia in Dunedin (from Clearwater, take Highland north--it becomes Patricia when you cross the city line into Dunedin). This is our favorite local Italian place, owned by a couple brothers. Their lasagna is to die for!
La Cabana del Tio, on Drew St by Duncan: This little hole in the wall serves the most awesome tacos in house-made tortillas formed and grilled while you watch. Bring cash!
Don Pancho Villa, also on Drew, has good Mexican food at decent prices. My stepdaughter raves about the filet mignon in chimichurri sauce, offered at under 14 bucks.
Cooters, on CB: If you like snow crab, go on a Monday or Tuesday for all you can eat of the best snow crab around. This isn't exactly cheap at 20 bucks, but it's a great value.
Paul's Pizza on McMullen Booth north of Drew: This is my favorite pizza in Clearwater (I also love Queen's Pizza and Cristino's). I understand they have a lunch buffet for under $6 bucks, although I haven't been there.
Also, check out the Sunset (AKA early bird) menus at some of the better restaurants in the area. For example, Rumba on Gulf to Bay at Keene offers a good value menu before 6 p.m. Sit outside on their festive patio if the weather's nice.
I also like Lenny's, mentioned above. Other good bets for breakfast are Wildflower Cafe on S. Fort Harrison and Benedict's on Alt 19 at the Dunedin Causeway (a good stop if you plan to visit Honeymoon Island and/or Caledesi Island while in town).
I checked out Placy's website, which was still functional, but made the mistake of not calling to verify. When we got there the place was gone. No sign, no tables, no nothing! We ended up going to the Pierogi grill. The Pierogis were fantastic! I wish they allowed you more flexibility with ordering (it is six of one kind, 12 of two kinds, no smaller orders of their sweet ones, and fixed choices for the mixed order. But the cheese ones were fantastic! The decor is odd.....Egyptian themed. When asked the server said the owner runs other such places in other countries that also serve Egyptian food. Very odd, but the food was good!
Well, once upon a time I would have enthusiastically recommended Lenny's, but the last visits have been mediocre at best. And you always have to wait for a table.
Lenny's was about the only place we drove to Clearwater for on a weekend for brunch. We just don't get up there often. I'm sure more local people will have some options for you.