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There is a wide choice of serviced apartments in Bangkok. Most but not all are located along the wider Sukhumvit Road area.
We would suggests you choose accommodation close to a BTS (skytrain) or the subway station. On the other hand, it may be useful just to be a few hundreds meters away from the main Sukhumvit road, to avoid a too crowded and noisy environment. Cheaper accommodation can be found on the outskirts of Bangkok, but we are not sure that is where you want to be.