Depends how close you want to go, your budget & type of restaurant/bar. If you walk north between the CN Tower & Skydome there's a Baton Rouge just across the bridge walking towards front street, they have great ribs and it's a more quiet steakhouse. It's probably the closest place to the dome and not always packed as most people jam in to the Boston Pizza right on Front Street if you keep walking (Avoid that unless you're there early enough). If you want to stay on Front Street for drinks, head East to the Loose Moose. Get there early for a seat though.
If you want more local dining, head north past Boston Pizza to King street. From there anything East for a lot of local restaurants.