For beginners/intermediate. Your best bet is either the petit saleve, or the trails around the river. I haven't done enough exploring to tell you other places yet sorry.

Hey there, there are nice trails in and around Verbier, and if you hire a Mountain Bike guide for the day you will be taken on routes that suit your ability, skill and fitness levels.  Nice views too, if you get a day without the clouds!

My husband is a qualified Mountain Bike Technical Leader in Verbier and can offer his services.  PM me if you would like further details. 

Thanks, Michelle

Psyang,

I agree with Mickey.  I hike around the river quite a bit and there are a lot of trails, not too technical, but still good for both hiking and mountain biking. 

Parts of this trail are really good on a bike and accessible from the City. 

http://www.myswitzerland.com/en/interests/hiking1/hiking-suggestions/top-hikes.html?region=010

The same website also offers some mountain biking trails as well, link here:

http://www.myswitzerland.com/en/interests/cycling/mountainbiking.html

I do not get out on the bike much, unfortunately, someone decided they liked my mountain bike more than I did when I first moved here and I have not got around to replacing it yet......

Enjoy