There are other much smaller places with fewer facilities and definitely more tricky transport for someone without a car
That is a very sweeping statement lacking in a lot of subtlety given the current bus services.
You don't actually say which rail route you are taking from York to the Lake District- there are at least 5 routes- via Newcastle and Carlisle, via the Settle/Carlisle line, via Preston, via Manchester or via Carnforth.
If you come up the Settle/Carlisle line and get your timings right it is possible to get off the train at Kirkby Stephen and take a bus from Kirkby Stephen station to Penrith for the bus onwards- with the best service on a Saturday.
The bus from Penrith to Keswick also stops in Threlkeld village every 30 minutes, in Braithwaite or Bassenthwaite every hour (alternate services).
All useful places to stay.
From Penrith Railway Station there are also buses every hour or two hours (hourly at weekends at that time of year when alternate services are open top) to Ullswater- Pooley Bridge or Glenridding.
Also from Keswick Bus Station there is the Borrowdale bus #78 every 30 minutes along the valley- lots of places to stay in the valley with many walking opportunities. That service is open top all year (even in mid winter, like today).
If you have come up the Settle/Carlisle or across from Newcastle there is also the 554 bus from Carlisle direct to Keswick via Bassenthwaite.
June is before the summer school holidays so Keswick will not be as crowded as it gets in high summer. But I am all for dissipating people away from what is a honeypot destination. That is one of the reasons why the Council is devoting a lot of money into supporting and improving the bus services.