Oh...some great ideas here...gotta give my cents in as well...kudos to stay at home dad..my dh was a sahd for the first 4 years and what a GREAT job he did!!
First, I really commend you on staying at home...post college I was a nanny for a few years and saw the importance of having a parent at home...it is extremely undervalued in our society..but I think that is changing.
My children are now 10, 7 & 6 and we homeschool. When mine were under 4...well, we had 3 under four so you can imagine how we filled our time!

Actually, we became frequent visitors at the library for story time...I found wonderful books to start reading to them at that age...my favorite authors for that age are Margaret Wise Brown, Cynthia Rylant, Diane Goode, Tomie dePaolo, Sid Hoff, oh there's just too many to name...but you'll start finding the good ones...one of my son's favorites was "Goodnight Moon"....make sure you look for the red balloon in each picture!

We would keep collections of wood blocks around...built sooo many things with those! Nature walks...take some snacks and bottled water and just let them explore a beach or a rocky gravel pit...they can amuse themselves and LOVE being with nature. Check around your area for events with orchestras...several events were planned for preschoolers to introduce them to the sounds of the instruments..also fun puppet shows and the such through performing arts centers.
But, basically, letting them create creatures out of homemade flour dough, giving them a wooden spoon and pots while you start dinner, load them up with tons of good sturdy books, have fun with finger paints, playing with sand and a bucket...just let them be a kid and they'll be happy.
Tara