I had just given birth when my son turned two... so we went for a small, family only party. I made the whole day about my son, though.
Early in the day, we went and bought a Blue's Clues balloon at a store (he loves Blues Clues)
For lunch, we went on a picnic at the park. (And lots of time on the slide, etc.... a nice, new ball from the 99 cents/dollar store might be a good gift
And then after dinner, we had a Blues Clues Carvel Cake for dessert. His favorite part was blowing out the candle.... must have done it three or four times.
No guests... just our little family and the baby. Don't think he felt at all deprived.
For gifts, he got a Travel Aquadoodle, some wooden blocks, and a Sit-n-Spin... all are still very much used/loved. We also bought him some bathtub crayons (which can be homemade as well)... for a special bday bath.
I've seen lots of Moms do the park thing... and we might do that for #3.
As for restaurants that are kid friendly, we've had the most success with chains like Denny's, Applebees, etc. But, there is a little french bistro that we've taken DS to since he was a few weeks old, where he's welcome as well.
Other things to consider...
beach (depending on where you live)..
My son also really loves his gymnastics class (especially the trampoline pit!) Might want to take your son for a free trial class to a gymboree, little gym, etc. type program for a new fun experience on his bday.
Bubbles are always popular in our house....
Also, consider doing foot prints/hand prints with finger paint as a craft activity. Great for the baby book and cheap