Eating out in Kasimov can be a problem, as there is insufficient supply of restaurants. A surprisingly good choice is Kafe Vechernee, next door to the bus station. A good choice of excellent food, very cheap (at least compared to Moscow), and reasonably good service. Claim (I did not check) that they are open 24h/24. Much recommended.
Favorite Dish: Okroshka - a national Russian soup which is cold and is made of kvas - a cold Russian drink, in a sense similar to coke, but still and without sugar - and vegetables. Though it may sound (and sometimes even look) unpleasant, it is actually very tasty. Served as soup (the first course).
The best if you have your own car or a friend with a car. It is 260 km from Moscow - about 4hr one way. Follow P105 to Egor'evsk and Spas-Klepiki.
If not, there are two convenient options from Moscow. First, take a train to Murom; there is one train which arrives 5:00 (you only sleep 5hr there). You then walk 15 minutes to the bus station, and either take a bus to Kasimov at 6:30, or have your time in Murom and take a bus 9:30. The bus takes 2h to Kasimov; the return bus is either around 15:00, or overnight. Second option is to do the same from Ryazan' (combining with a day in Ryazan') or Sasovo.
I did the Murom option and wanted to take 15:00 bus, but liked Kasimov so much that stayed the whole day and took the overnight bus to Moscow.