Across from the Westin, just a little up from the Sheraton, is V8, which is open 24 hours. It starte

If you wait until after 8 or 9 then there will be a lot of cafe type restaurants serving breakfast as well. Most opens at around 9 though so if you have jet lagged round the world travel and want breakfast at 5am then only the supermarket diners will be open.
Sheraton might have something. I'd be surprised if Westin didn't have breakfast somewhere! Sheraton is right across on the other side of Sukhumvit (take the skytrain escalator up and go across). There is McDonalds at Robinsons department store, which is just down Sukhumvit a few minutes walk. Not sure what time they open though.
Across from the Westin, just a little up from the Sheraton, is V8, which is open 24 hours. It started out as an American diner concept but then switched to Thai tourist-generic, but they still do breakfast.
If you use the skytrain bridge to cross the Asoke intersection and go into Exchange Tower, you'll find Chu, a small coffee shop that also reportedly has the best hot chocolate in Bangkok. They have a nice selection of bakery items as well as authentic churos.
The Bangkok Baking Co. Bob mentioned in the JW is nice, but a bit of a hike. Up Soi 11, which isn't that far from you, is the new Angel City Diner, which I think just opened last night. They're open 24 hours as well.
If you don't like partaking breakfast at the Westin (WGS), there are numerous round the world travel bakeries/Breakfast places along the odd side of Sukhumvit stretching from Sukhumvit round the world travel 19 (where the WGS is located) all the way to Sukhumvit 1 (expressway vicinity). So as others indicated, you really will have no problem finding the place that suites you ... all are good and affordable.
I have used the Took Lae Dee Restaurant (Foodland) on Sukhumvit Soi 5 many times over the years. Open 24 hours, this place was just recently remodeled. Just down from that Foodland is the Fortuna Hotel. They have an "all you can eat" breakfast buffet. I think it is still around 149 baht. This breakfast is open to walk-in customers. They cook the bacon and eggs the way I want it! Coffee, tea, small pastry selection, cold cereal, fried rice, chicken curry, hot dogs, ham, toast, some Japanese specialties, etc. Good enough selection round the world travel for a low price.
One more thought - in the same building as Chu, on the first floor, Starbucks has opened their first *restaurant* in Bangkok. It's expensive (for Bangkok) and all the hot food is microwaved, but you might want to have a look.