Heids is a definite. Also was going to go to Coleman's. Graduated from high school with Pat Coleman. I will be staying on the west side, Westvale/Onondaga Hill area...
I am on that side of town, there are a ton of options.
Twin Trees is an absolute must, go to the original on Avery Avenue, it can get crowded but the Pizza is outstanding and the rest of the food is good. The immediate Area surrounding the place is a bit seedy but I have never had an issue.
Also if you like Mexican try Azteca Grill, its located in a small plaza in Camillus across from the large Home Depot Plaza. Good prices and a large menu selection. Get the Nachos with cheese, they use this mexican cheese that is out of sight. Also have good frozen Margaritas.
As mentioned earlier, Limp Lizard is right across from Western Lights Plaza and is a great place. Oddly I have never been a huge fan of there BBQ, though I recommend there pulled pork nachos. I haven't had there ribs in sometime and for a pulled pork sandwich Dino to me is still king. To be honest I haven't had great ribs in Syracuse in a long time, be it local joints or chains its been difficult to get a real nice rack of ribs. Amazingly Kirbys in Westvale plaza was probably the last place I had good ribs, I would recommend them to. A little bit more upscale, not fine dining but not Tullys either. Back to Limp Lizard I highly recommend any of there sandwiches, burgers and especially the BBQ chicken. My fiance gets the chicken every time, the last time it was the best either of us had ever had. If you go there get there cornbread as a side, very good.
With kids you cant go wrong with Tullys, I am assuming you have been there before, if not I would recommend it. There Tenders are like crack and they do good burgers and sandwiches. They have a place in Fairmount but watch what time you go, place is always jammed.
Couple of other thoughts: If your looking for something quick Fish Cove in Westvale Plaza is a nice option, there fish sandwiches are crazy good and they have pretty much any side or other seafood (shrimp, clams, smelt, oysters) available by the pound. I would have recommended a burger joint Cheeburger Cheeburger as a great family place (awesome burgers to) but they were just seized for failure to pay taxes, sorry to see the place go. You might want to consider a jump over to Carousel (Destiny USA) mall as well. Its mostly chain places but they have a ton of options now from Gordon Biersch to Toby Keiths to TGI Fridays, Melting Pot, PF Changs etc. Dont forget about Erie Blvd, you could cruise up and down each side and have your choice of different places ie Texas Roadhouse, Koto, Secret Garden, (several Thai/Korean Restaurants), Delmonicos, etc.
If you guys like Thai there is a place called Bangok Thai on Old Liverpool road that has good food and its not far from Heids at all. There is also a new BBQ place in Camillus down the road from Azteca Grill called Moes. I did try it and thought it was OK, the fiance wasn't impressed but we didnt try the ribs or brisket just the chicken and pulled pork. There is another BBQ joint in the village of camillus Krabby Kirks good food and they have a nice sized deck outback, though there is not much view if you know what I mean. I would also recommend the Waterfront out in Brewerton, short drive and having lunch or dinner out on there Patio with a summer cocktail is a great time. Good food to.