Hi -
Much is made by Mr Steves of using Keswick as a base for the Lake District and to be fair it would suit your purposes - small town, plenty of easy walking nearby. It does get incredibly busy, as does the majority of the Lake District, so early booking is a must.
Other places you might consider include Grasmere, further south, which would also suit your purposes but because of the Wordsworth connection it also does get very, very busy. Coniston, further south is a favourite of mine but can only be described as a large village and I have a soft spot for Langdale (Elterwater is the only real ‘village’ thereabouts). I would be inclined to avoid staying in the Bowness/Windermere and Ambleside areas - worth visiting for sure, but to many this IS the Lake District and it can be something of a trial to base oneself there as it attracts literal busloads of day trippers.
York is a good hub for branching out in all directions but if you’ve never visited before, York itself has plenty of attractions to keep you occupied for the duration of your stay. And it is a very ‘walkable’ city. However, you could branch out to Ripon, and just beyond, Fountains Abbey with its formal water gardens (be warned, it’s not a flower garden per se so isn’t the colour riot you might be wanting). Heading north east there are the North Yorks Moors - Helmsley has a Castle ruin and not far away are the ruins of Rievaulx Abbey. Pickering is home to the North Yorks Moors Railway which will take you through the moors to the east coast at Whitby if needs be, by steam hauled train if you plan carefully.
Going south east you’ll encounter the not much visited Yorkshire Wolds, which we walked through recently - we were very taken by Thixendale and the confluence of the dry valleys there, quite unlike anything else in the area. It was my first visit there and I’ve lived in Yorkshire all my life. That said, there’s not much else there - big fields given over to farming - feels remote if not wild.
If you need more information on these northern areas please feel free to ask, either here or by pm. Hope you get the information you require and will have a great trip. Fingers crossed for half decent weather!
Ian