No matter where I've stayed in San Jose, traffic noise has been an issue - if I was building a place in San Jose, I'd put in hurricane impact windows, but the issue is because of the great climate, you want the windows open - the noise sucks; its one of the downsides to staying in San Jose (but other things make up for it)
Truly.....if you are a light sleeper, bring ear plugs, take a sleeping pill (prescription or over the counter, or even herbal).
Lets list the annoyances you can expect (better say will encounter, b/c while you may not hit all on the list, you will hit more than a couple

) to encounter staying downtown San Jose:
Motorcycles - they are charged less in registration fees for a smaller engine, and they make up for it by over revving what they do have - very annoying; like a dentist drill
Car Alarms - whether they are being towed, or stolen, you will very frequently hear alarms
Street noise - from people walking, or talking loudly on the street, to trucks - you will hear it all
Bar noise - while not open all night <thank god> bars think nothing of blasting their music until they close.
Whores and their shoes - yup - the little cunts pound up and down the street, probably trying to attract attention.
Car horns - all night, every nigh - let a car be a nano second late in taking off from a green light, and the horns start.
For a society that in general prides itself on its manners, you would not know it based on the nonsense you endure staying downtown San Jose.