The closest to the Embassy is Bayview Park Hotel, right across the street plus the distance if you need to walk to get to the pedestrian overhead crossing bridge. It is pretty cheap if you can get a good deal, and what I like about it is that it si very safe with a doorman whi keeps a careful eye on who comes in and leaves, and lots of cameras, room vault, But the free breakfast is terrible, and the rooms are a little old and outdated, and the pool is tiny.
There may be many airbnb that are even cheaper, but I'm not a fan of the airbnb's that I've checked out in that are .. mostly due to no doorman, slow elevator, creepy hallways, check-in, etc... But perhaps there are some nice ones?
On the last visit, we stayed at Diamond Hotel. It is the most expensive hotel in that area, but still was only about $110 including a great breakfast spread, .. for me the extra cost was worth it. But for a simple stay Bayview Park will be good enough unless you want some luxury. The really even cheaper hotels in the area are probably just fine, but I wouldn't stay there myself. A little farther away there are a couple of similar and decent hotels as Bayview and with better breakfasts. Depends if your priority is to be as close as possible to the embassyl