"In transit" means that the main purpose of your 'visit' is as a stopping point to get from one place to another. I find it helpful to ask two questions:
- If there was literally nothing you wanted to see or do in the place you are coming to (New York) would you still be coming there?
- Are you spending as little time as reasonably possible there to achieve your transit?
If the answers to both those are "yes" then you can confidently say you are 'in transit'. If the answer to either is 'no' then you might be better off stating 'tourism'.
If you were arriving on a cruise ship and departing on the same cruise ship (and could reasonably have stayed on the cruise ship) then question 1 would be answered 'no' and you are not in transit. You should choose "tourism".
Being in transit does not stop you doing tourist stuff while you are there. Also if you are a UK citizen it is unlikely that the answer will make a difference to whether you are granted an ESTA or not. And in any case, stating on an ESTA 'In transit' as the purpose of your initial visit does not prevent you using the ESTA for other purposes later on.