I used to live in a cotswold village surrounded by countryside.
Now I live in Swindon.
Ironically, I can do more walks in Swindon than I could in the village (well, apart from less than a mile walks round the village)
Here, we have dozens of cycle paths, which are for use by cylclists and pedestrians, and are mostly used by people walking. So from the end of my road (20 yards) I walk on paths with grass each side, so not pavements or roads (although I have to cross roads). Within 10 minutes I can be in one of these places:
-nature reserve several square kms of woods and fields, some gravel and paved paths so you can do as muddy or not as you choose.
-disused golf course which has been returned to nature, fields, wooded bit etc
-go through the golf course for a longer walk and go along a river, and then onto a wooded/grassed hill which is a nature reserve
- a canal path leading to fields and a lake
-river/grass and then woods leading to an urban forest, still in the planting stages, so quite open.
-lots of local green areas, playgrounds and parks, all linked by the cycle paths.
I had no idea all these places existed until we got a dog. Well worth exploring unexpected places, and seeing what is actually availble. Rural doesn't necessarily mean good walking, it depends on which paths there are and if they are maintained.