J.V.
Hello! Congrats on your new baby. I have a son that was 2 years 9 months when my daughter was born. I nursed too and it took about 1/2 hour or so most of the time. She also ate every 2 hours. When she was a newborn, I didn't really take her off unless I know she had fallen asleep.
As far as activities for my son----we played red light green light, where I would be nursing and tell him to stop when I said red and go when I said green (we have an open concept house). Also Simon Says (he didn't quite understand the concept at that age). I also had him sit on my legs (they were up on the rocking chair's foot stool) and read books. Those things seemed to work the best, I can't really think of too much more that we did.
My husband and I tried to think of everything possible I could do with my son and put them all on a list on a dry erase board on the fridge. That way if I needed something quick, I could look up there and see what would fit the situation. Hope this helps!