Esther, we're on the same page. I already know my DD will be glued to what ever the current electronic device is of the time when she gets older, I'm going to try to hold it off as long as possible!! She can play with her imagination and learning toys in the mean time. She doesn't seem to be missing out on anything, IMO.
I think moderation is key. I think it's important for kids to be exposed to a variety of learning tools. Josh has a MobiGo and I find it's been good for him. He has a handful of games and they have all been helpful in helping him learn skills like counting, recognizing letters, etc. It's fun and age appropriate. It does come in handy during long car trips or when a little down time is needed.
I do let Weston use my phone here and there, but I try to use it as a last resort. Today I went to lunch with a friend and he was being a bit rambunctious with his friend, but rather than pull out my phone, I got him engaged in coloring his kids menu and just kept right on him to not let him get out of control.
That said, he does like to play games on it--and I have some fun educational ones too he really likes. But I limit screen time to a short amount of time.
I'm kind of in the middle. Sophia does not have her own device, but she has lots of games on my iPhone and I let her play them at certain times. I rarely let her play in the car, because I would rather her talk to me, look out the window, sing, use her imagination, etc. If it's a long trip, it's one thing, but I don't want her glued to my iPhone every time she's in the car (and she would be).
It's the same reason DH and I specifically chose not to get a DVD player in our car. We don't want her watching TV/movies when she's riding. I see the point on the day and age we live in but I also want my child to develop her imagination and to know how to entertain herself without a screen in front of her face. So I agree, it's all in moderation, and for me, that means not more than 30 minutes maximum per day of video game time at this age. She can get that on my iPhone so I don't really see myself buying her a Leapfrog but I haven't looked into them much to see what all they offer. I feel like I would rather wait until she's a little older.
As for restaurants, we only eat out one time per week and it is our "family date night" so we try to keep the phones put away and actually talk to each other I find if I interact with Sophia I can keep her fairly entertained, and we try to go to restaurants that are at least somewhat fun for her.