The Lake District is beautiful, especially in early Autumn.
Tips ... well, the main transport hub is Windermere, as there is a train station there and lots of buses and boats to whizz you around. However, it's a pretty busy place, and quite touristy, with all the good and bad that brings.
If you want somewhere a bit quieter, I'd second the others' recommendation for Ambleside - a short bus/boat ride or cycle from Windermere.
Otherwise, Keswick is a really nice market town in the northern part of the Lakes.
If you are really into biking, you might want to get the train to Grange on Sands (quaint genteel seaside resort) and cycle up into the Lakes from there, via Coniston, and then pick up the train in Windermere at the end of your ride. It'd be a long ride though!
Have a look at the National Park's website for the official 'non-commercial' view on what to see, how to travel and where to go.