I used to live near here. My recommendations would be;
Calke Park - a beautiful National Trust estate very close by with a great house, cafes, walking etc - the house is very interesting as it's been left as it was and has some lovely collections in there too. It's just lovely here and quickly becomes a favourite of people who visit.
Staunton Harold - close to Calke Park. Nice for a potter. Courtyard with cafes and little shops. Lake and walks from there if you are so inclined (you can link up to Calke Park if you want to.)
Melbourne. Pretty little village with a lake and tea room (less to do here though.)
The Peak District is realistically over an hour away but is so, so beautiful. You would be spoilt for choice there. Avoid Dovedale if you don't like crowds of tourists but loads of gorgeous villages and places to visit.
If you have children then Foremark Resevoir has a great play area next to it and a cafe.
Accommodation wise - there's a very nice bed and breakfast at www.breedonhall.co.uk which is very close to EMA. We have stayed here. Lovely room and delicious breakfast (although it is in their big kitchen with the owners so if that's not your thing then maybe not.)
Otherwise I only know Premier Inn at Ashby de la Zouch. You know what you are getting there I suppose! There is a castle at Ashby which you can walk around (it's not that well preserved but you can climb the tower and look out.) Might be English Heritage?
Have a nice weekend whatever you decide to do!