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Moreton-in-Marsh is the hub and the easiest base, but it is not the only station on the line. The same GWR train from Oxford or Paddington calls at Charlbury, Ascott-under-Wychwood, Shipton & Kingham before it reaches Moreton, so if one of those suits what you are here for, you can get off earlier without changing trains.
Charlbury is the pick of them. The station is in the town rather than a taxi ride out, which is rare down here, and it drops you next to the Wychwoods. Kingham is marketed as the gateway to the Cotswolds and is the nearest station to Stow & Chipping Norton, though you will want a bus or taxi for the last bit. Shipton serves the three Wychwood villages, and Ascott-under-Wychwood is a request stop, so the train only calls there if someone asks.
None of this replaces Moreton, which still has the 801 bus on its doorstep and the widest reach once you arrive. But if the eastern side is what you are after, the line gives you more than one front door.