I am puzzled, presumably you knew that what you wanted to do would fill three days before you booked it, or are you asking for us to prioritise your list, if so what list?
There are reasonably regular coach/bus services between Heathrow and Oxford and, short of paying for a very expensive taxi, these are the most convenient way to make the journey. Just google "bus heathrow oxford".
To be honest the top ten really depends on your interests - be it museums, architecture, gardens, historical sites, film & TV locations etc, etc. If you are more specific about your interests then we can make suggestions.
You can do a lot in 3 days. I would definitely take in the Ashmolean (closed Mondays) and Pitt Rivers. You can tour a college, go on an evening ghost walk, visit some historic or literary hangouts (Eagle & Child, Turf Tavern pubs), walk along the Thames or canal from the city centre to waterside pubs etc, spend an evening at the theatre etc. There are numerous walking and open top bus tours.
Oxford is also a compact city so if you are able, seeing it on foot is great.
Probably the best thing to do is head straight to the tourist info centre on Broad Street.
Let us know what sort of things might particularly interest you and we can give more specific advice and recommendations.
As previously suggested, the bus from Heathrow is most convenient. Let us know where your hotel is and we can advise on which stop to ask for when you board.
When are you going? I would recommend hiring a punt from Magdalen Bridge, but not if you're going in November.
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