In that situation I'd probably opt for the parallel street.

Sometimes when I take a certain route home I am riding along in 3 lanes of stopped or slow moving cars and I have to turn left after about 1/2 mile of riding through this area so I just take the right lane and then get over when traffic slows to a crawl and filter. I ride a road bike with 42cm handlebars so I can fit through some pretty narrow gaps.

The sidewalk would be my last resort...actually, it wouldn't even be a place I'd consider riding at all.