Ok, if I wanted to avoid mainstream music, what would be your recommendations? With wich bands or artists should I start with that are not mainstream right now?

Here is a list already compiled by Satchmo of what you SHOULD listen to. It's a great list of bands to explore and I couldn't do any better.

http://www.radiomute.com/398804-post2.html

You might want to start out by finding some bands that you like and seeing what bands they themselves were influenced by. Often times the bands that you favorites bands are listening to are much better.

Check out the list, and I will make mention of the band I always recommend to those looking for stellar non-mainstream music: Morphine. Start with Cure for Pain then onto Yes.

I'm uncertain of what style you dig, though by your avatar I would assume that you like what's best
With that, I also recommend the original Fleetwood Mac, Peter Green's Fleetwood Mac. Start with the 1968 debut album, often called the dog and dustbin album, then English Rose. Follow up with the remaining two Peter Green Fleetwood Mac albums (Mr Wonderful and Then Play On).

Some of my favorites are Coldplay, Travis and Radiohead, but how can I know their influences?
Anyone in special from the big list to start with?
Meanwhile I will check out Morphine and Fleetwood Mac.
Thank you everybody.

Remember, Peter Green's Fleetwood Mac.

Based on that you should also like these (dunno about the non-mainstream part though);

Muse - Absolution
Vast - Music for People
The Decemberists - Picaresque
Madrugada - The Nightly Disease
Anathema - A Natural Disaster
Opeth - Damnation

Thank you all for your recommendations.
I have downloaded two albums so far: Cure for the pain and Absolution. The first one is very original, and I'm digging a lot. I do like Absolution too, that one is very similar to Radiohead in the good sense (exactly my taste).
I'll keep listening to more recommendations later and tell you what I think of them.

Good work, my friend!

For the record....any Satchmo list is generally in order of recommendation. Of course, when it's lists as long as those....after a while they're mentioned as they come to me; however, you're good to go if you go in order from the start.

Some influences of Coldplay and Travis are The Smiths, Echo & The Bunnymen, Stone Roses, House of Love, Chameleons