The Santa Monica bus (
www.bigbluebus.com) will drop you off pretty much in front of the building. I believe the #2 line is the one that runs down Wilshire Blvd. The Big Blue Bus covers the entire west side of LA, so if you find a hotel in the area you're most likely never more than a few blocks from a bus stop.
I've heard good things about the Best Western Royal Palace Inn & Suites on Sepulveda Blvd. My parents stayed there for a few nights, and said it was a decent place. This was a few years ago, though, so you may want to get some current info on it, just in case it's gone downhill since.
When you're at the consulate, make sure you peek down the block and wave at my old high school.