Lyon---3 nights in May ---which arrondissement? --- urban atmosphere ?

It would help if you could describe what it is you plan to do during the time you will be in Lyon.

In addition, if you could describe what you mean by "budget accommodation," that would help as well. For example, if you were to visualize "budget," is there a particular amount of money that you would have in mind?

Ideally, I’d probably stay in the Old Town. All your budget accommodations tend to cluster around the main train station (Perrache)? This isn’t a particularly nice area, but you can easily hop on any metro/tran lines at the station and get anywhere in Lyon in a jiff. It was fine during the day, but I would consider taking a taxi there at night. Lovely city, enjoy.

I think you could find something reasonable and comfortable in the Presque Isle. It's walking distance from there to the old town, has an urban feel, and is served by metro and bus.

Don't ignore Lyon's great bike-share service, if you like that sort of thing (I do).

A good guidebook is your best resource.

If you can handle stairs (there's not only no elevator, but the lobby itself is up a flight of stairs), I recommend the Hotel du Theatre: http://www.hotel-du-theatre.net/. It's very centrally located and in your price range. I had a great stay there, but it was about 10 years ago; I see that Rick still recommends it in his France book.