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Park Inn is cheap and crappy 3star close to Old Town. Blu City Centre is closer to the Old Town, but I think Olympia was renovated later. I personally would skip all of them and choose Swissotel. Or Telegraaf in Old Town if you want to be close to nightlife and cruise tourist hordes.
All of them are about 5-10 minutes walking distance apart and about 4-8 min walking from Old Town. Central is nothing to write home about and not very classy, but in a quiet spot and some of their more expensive rooms have big balconies. Olympia was once highest building on Tallinn (it was built for Olympics back in 1980) and has still certain charm, while Blue City Center has nice lounge (and open terrace) with unbeatable views on the highest floor.