Hey dosimeter! I did my undergrad at UW. Though I don't have a ton of information on housing, I will say that Langdon Street is frat row. It's not awful, and the houses are gorgeous (it's a historic corner of Madison). But there will be parties.
I know grad students live in Eagle Heights/Shorewood Hills area (west of campus, probably pricey), and also over by Quarry Park off of University Ave (also west of campus). Buses connect to campus. Lots of people live south of Union South as well, even as far as the Vilas neighborhood (towards the zoo/Monroe St).
I will say the farther up on Langdon (further from campus) you are, the less crazy the parties are. I can't be certain, but I think I actually knew somebody who lived in Lake Towne Apartments. All I really remember is that the hallways always smelled like weed and cat litter, and once his heater broke and it took an obscenely long time for the landlord to even come in and look at it. The apartment itself was fine. Quiet enough (next to a sorority, if I remember correctly, and they were sometimes loud) and a good size for a studio.
I hope this was some help to you. Good luck with your search!