Don't forget to make an appointment on the embassy website. They won't see you without one.
Nereus is the local more or less for that area. I've never noticed a hotel on Wireless, just embassies and corporate buildings, and condos/serviced apartments, but not looking too hard. Pete
Governments are instituted among Men, deriving their just powers from the consent of the governed. Source
It's a really short walk from the Phloen Chit BTS station to the US consulate on Wireless Rd. So, pretty easy to stay anywhere that has access to BTS. I always stay at the Honey Hotel (1000 baht) on Suk Soi 19. Short walk to the Asok BTS, short ride to Ploen Chit, short walk to the embassy.
That said, there are many not-so-cheap hotels nearby: Conrad, All Seasons, Plaza Athenee, Okura, Oriental, etc.
I used to stay at a place called Jim's Lodge on the small street directly behind the embassy. I used Agoda to book it so you can check there to see if it's still around. It's a short walk around the block to the embassy, plus there were a couple of small hidden restaurants nearby that were good. It was only about 800b per night when I stayed there.
My brain is like an Internet browser; 12 tabs are open and 5 of them are not responding, there's a GIF playing in an endless loop,... and where is that annoying music coming from?
Jim's Lodge is still there on Soi Ruam Ruedi. You can get to the consulate by either walking south toward Lumpini Park and then up Wireless or you can go north and cut through The Conrad to Wireless and then down Wireless to the consulate.