Personally, I think doing the "new GB team in another city" route is probably wisest...and to be brutally honest, I'd prefer to avoid involving any of the surviving original cast/characters as much as possible, with maybe a few minor exceptions as cameos: maybe a phone conversation with Janine about starting up a new GB franchise, or a montage like in the first two movies with interviewers asking certain figures about what they think of this new GB team starting up - and one of those figures is Walter Peck.
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Also, I wouldn't employ the theme song until the end credits, although I'd probably stick with the Ray Parker Jr. version of it; they already tried doing a rap version of it in GBII because it was the 'hip' and 'trendy' thing to do, and it hasn't been heard on the airwaves since, whereas I'd be willing to bet that most pop radio stations that have '80s blocks have had Parker's "Ghostbusters" pop up occasionally. On a similar note, I think Chicago would be the best locale, primarily because that's where Ramis was from. That and dedicating the movie to him I think would be a fitting tribute.
There's one other nod I'd throw in, too: I'd make the new GB vehicle an SUV or an ATV or some Humvee-looking thing, both as a nod to the RV in "Stripes" and a parody/spoof of the Tumbler (frankly, I'd love to see a high-speed chase sequence with a proton-cannon mount atop the vehicle firing away at an escaping ghost and causing almost as much destruction as the chase itself does). For that matter, some new hardware with a slightly more militaristic touch: proton-pack miniguns, grenade-traps (you'd toss it rather than slide it, the shell bursts on impact with the ground and an energy-field blasts out of it to contain the ghost and pull it in, shell closes back up), possession-proof vests, etc.
