Coldfeet
In terms of schools and choosing between Oakham and Stamford, after we moved to Stamford, my DS had to go by train to Stamford every day, because he only had one year left and was in the middle of his GCSE's, but my DD changed schools and went to Casterton College (it's actually Rutland authority, but we live this side of Stamford closest to CC anyway). Casterton at the time was an Outstanding Ofsted school! (and now it requires improvement apparently). However a lot of my daughter's classmates applied for 6th form to Bourne Grammar school and got in.
In terms Leicester being nearest city - that was one noticeable drawback for me after moving to Stamford, nearest city is Peterborough, which I really really don't like. I tried to drive to Leicester a couple of times, but it was just ridiculously far away compared to Peterborough, and Peterborough has all the shopping I need anyway, so it was difficult to justify. However in terms of universities, Peterborough has none and Leicester has two.
While Rutland is nearly 100% white (for the Catmose College's production of 'Hair' the role of a black boy who sings about being black and singled out and misunderstood had to be performed by a white boy
, there was no one of enthic minority at the whole big secondary school - at the time anyway), Leicester has schools where there are no white pupils, it's more diverse than London. Some people don't like it, but in any case it is a proper city and far more vibrant than Peterborough.
If you think about getting a job in Leicester, take a look at Uppingham, it's even smaller but it's charming, has good schools and closer to Leicester. However it has no train station. But only 6 miles to Oakham and its train station if you need to.