Well there is a lot of interesting architecture within Nottingham Center itself.
Consider -
The Park area;
The, apparently, oldest public house Ye Olde Trip To Jerusalem,
Nottingham castle,
Nottingham caves,
Brewhouse yard museum,
and the area around 'the park' there is some good architecture.
Then the lace market with,
National Justice Museum
Good church (pub) at Pitcher and Piano
Lots of good architecture around the old lace market
Just on the outskirts of the city;
The Arboretum
Greens Windmill
Just outside of Nottingham, and easy public transport, there is;
Wollaton Hall (Batman film)
Attenborough Nature Reserve
Not so easy but achievable, Southwell minster
Could consider Castle Donington for the aero park and race track, plus museum of cars.