We are planning to go to Keswick from Leicester next January. I am not sure which is the best way to travel there. I would prefer not renting a car but I am open to it if it is the best way. I am failing to find any train tickets available (from Leicester to Keswick(Bus Station)).
The train doesn't go to Keswick. You should buy a train ticket to Penrith and then take a local bus. Check on http://www.traveline.info as it's the best website for public transport in the UK.
A National Express coach journey from Leicester to Keswick, with a change in Birmingham, will take about 8 hours and set you back £50 for a single.