I seriously enjoy taking my bike out into the sprawling fields near where I live. Just riding along the dirt tracks and enjoying the isolation from the world is incredible. Quite often I feel as though I'm the only person in the world, rather humbling at times.
From NE Tennessee...favorite place to ride is a local SORBA park. Has a ton of fun trails with different levels of technical difficulty. The scenery is gorgeous, from mature forest to creek bed, to lakeside, etc.
I live in Calgary, Alberta, right next to the Rocky Mountains. I usually ride in and around Fish Creek Provincial Park, but my favourite rides are in Canmore, Banff and Fernie, BC.
there's a lot of great bike tracks around my town of Adelaide, my favorite is a path that goes from the city to the beach along the river, it's a great ride with amazing scenery all the way...I love visiting the city & chilling at the beach for a swim on a lovely day
I like to ride a variety of places if I'm on my road bike - then it's just some of the local street bike paths or rail to trails. If I'm on my hyrbid, I'll head to parks and combine it with birding.
In Connecticut (US) I like to ride my racing bike on the Farmington Canal Line (a rail-to-trail - no cars!).
For MTB the best place around is SOR (Single Tracks of Rockland -- 650 acres of amazing singletrack in the Rockland Preserve).