If you wish to 'do' Richard III then you can buy a joint ticket for entry to the battlefield and Leicester exhibition. I would be inclined to visit in that order, the Battlefield Centre gives a good overview, introductory displays and there are AV posts as you walk round the field itself. The story of finding the burial site under an R (reserved) in a car park and the battle history itself is fascinating and both exhibitions interesting. On a weekday you can use the P&R by J 21 for the 20 min ride into the Leicester city. It terminates adjacent the Holiday Inn and then a 5 minute walk to the Exhibition Centre which is immediately opposite the cathedral as mentioned above. Out of peak the P&R is 3.50 return per car group, or £1 each for concession card holders, but no service on Sundays. (I happen to live locally and have no connection with any of the services mentioned!)
Sounds like you could submit a 'weekender' article for the magazine when you've';e done!