There's a Suzuki dealer in central Istanbul. It's on the main road very near Tophane tram station which is just across the Golden Horn. Assuming that you're staying in Sultanahmet (it's where all the hotels, guesthouses and hostels are) it's incredibly easy to get to which is no small consideration as Istanbul is simply VAST! Can't remember the name (sorry!) but am sure one of the Turkish members on here will know it - they're quite an organised bunch.
If you do stay in Sultanahmet try the Istanbul hostel. They're really nice and we stayed there this summer (for a long period after my wife was hit by a cab!). Nowhere in Sultanahmet has off street parking that i'm aware of but the Istanbul hostel is right opposite the Four Seasons hotel and so we parked on the corner by it and took advantage of the 24hr security and doormen - it helps that they're all bikers too so the guys at our hostel would take me over to help with any problems we had. The guys at the hostel sit opposite all the time for added 'eyes' and are very protective if they know the owner. The whole area's now some sort of pedestrianised zone so it's pretty quiet - a rare thing after riding through the city! If you stay there a practice run on the metro will run exactly along the route and pass the dealer so you'll know exactly where you're going.
One thing, do get in touch with them (they speak English and give them advance warning about the part you need as we found that some parts had to be ordered in and took quite a while (fortunately time we had!)
Hope that's of some help, but if you need anything more get in touch.