Hands-down, the best places for breakfast in Nashville are the Pancake Pantry on West End (not too far to drive from the Sheraton), and the Loveless Cafe which is a drive if you want to stay in downtown Nashville. We have the Nashville Zoo at Grassmere ($9 for your 3 yr old, free for the 10-month-old, $14 per adult). There is also the Adventure Science Center ($12 adults for general admission, added fees if you want to see the laser shows or planetarium, $9 for your 3, free for your 10mos in your lap). Just some ideas!
Also, the Frist Center is within walking distance of the Sheraton. It's free for kids under 18, $8 for adults, and they have a floor devoted to kids where they can explore all kinds of hands-on art activities and even create a digital portfolio. My hubby and I explored it when we found out we were preggo, and it's something our DS will enjoy when he's a tad older!
Noshville (yes, with an o) is a great place to eat. There's one on West End and in Green Hills. Adventure Science Museum and zoo are good choices for your kids.
Re: Visiting Nashville