Another good place near the Doubletree is Enriqueta's (2830 NE 2 AVE). You can get a very filling, authentic Cuban breakfast for cheap. Example: if you get there before 11 a.m., you can get eggs scrambled with ham, bacon or sausage, a delicious cafe con leche, cuban toast and orange juice for $3.75. After 11 a.m. the price goes up to $5. The sandwiches are great too. Just one caveat, authentic Cuban food = greasy for some. A lot of reviewers say it's the best Cuban breakfast and sandwiches in Miami. While that may be exaggerating a bit, it's safe to say (imo) that it's the best place for Cuban breakfast and sandwiches in the area.
Breakfast can be had at several places. Good breakfast in that area, however, is a bit tricky.
You could try Out of the Blue on 24th and NE 2nd for a more traditional brunch in an untraditional setting- a blue house in a still somewhat raw area.
You could have eggs/bagels at The Daily on 19th and Biscayne. The place can be deafening and does not have a brunch, per se. You order your dishes at a register and they bring them to you.
If you're willing to go to the Design District, you could try Brosia on Sunday (they only have brunch on Sundays).
If your'e willing to hop in a bus or a cab, you could go across the Venetian to A La Folie and have lovely crepes.