We are grandparents raising grandchildren too. My husband gets to play with the kids while I do the mundain things like cooking and laundry...LOL.
He plays Lego's, we have both Duplo and regular Lego so he has had the appropriate size for his age (they have new sets that have grandparents as the people), regular blocks (if he's handy with tools he can cut them himself in different shapes and sizes), Play-Doh, coloring, finger painting (sometimes we used pudding so it was messy and edible, the milk does stink when it starts going bad so it's a throw away craft), playing tickle, Hot Wheels, there are lots of simple games on-line at palces that are educational (links below), making snacks, cleaning chores made into games, watching an air popper make popcorn, he can build a water activity table from PVC pipes and a plain plastic tub from Lowes (always supervised, and we empty it after every use, it's a drowning hazard), wood puzzles if you can get them, the cardboard ones just don't last long, go for hikes (walks) and find items to put on a poster, scrapbooking a family memory book, plant an indoor garden, kick/toss the ball around, there are just so many things they do together. When he shows interest in riding a regular bike you might want to take him to BMX races and see if he is interested, it is awesome exercise for everyone in the family. My best friends whole family races and they started just a couple of years ago. It's so funny to see the...um...older gentlemen beat the pants off the younger men in their class. T-Ball is an option for this Fall, check in your area and see if they have to be 3 1/2 or 4. It is the best frun for the whole family. Our, now 6, girl played and we just took the double stroller and took everyone to watch her game. Soccer usually starts at 4 yrs. it teaches so much too. My husband has physical limitations so getting out and running with the kids is not an option but he still helps them learn to kick and catch.
It's good he wants to spend time with the little one,another thing you can do is ask you childs teacher what are some things they have in the classroom that your little one is fond of. When I had my childcare center I was often asked that question around Christmas time.
There are tons of ideas on the internet if you type in "activities for a 3 yr. old". I am adding some links now but wanted to tell you that you are awesome for taking on this responsibility. For me, it is so much better this time around. I find myself focusing on much different things since I am older and have more life experience.
Good TV shows and movies for younger kids:
We love anything that has to do with Lazy Town, Dora, Diego, Sesame Street, shows on Nick Jr., the movie "Cars", there is a whole line of Hot Wheels size line of cars from the movies also a size just a bit larger, "Underdog" the movie from jsut a few years ago, "Aurthur and The Inviisibles", QUBO shows like Jane and the Dragon or 3-2-1 Penguins or Veggie Tales ( this one often has religious based themes so it really teaches morals and choosing the right choice), and just about any Disney/Pixar movie.
http://www.nickjr.com/games/all-shows/all-themes/2-3-year...
http://www.mostlymommies.com/games.html
parentcenter.com
http://www.robynsnest.com/3old.htm
http://www.fisher-price.com/fp.aspx?st=30&e=gamesland...
I know this is long but I don't want to leave anything out!!!!!
Have fun!