Can I return to UK within 1-3 months on a 'tourist visa' after expiration of a 1-year academic visitors visa?

There are no relevant cooling off periods for an Academic Visitor, so the answer to you question is: yes, it's ok to apply at a port at a UK port of entry as a visitor in theory. They do have the option, however, to refuse entry based upon several clauses in Appendix V of the rules and you should be aware of these...

The first is V 4.2 (b): will not live in the UK for extended periods through frequent or successive visits, or make the UK their main home. They will worry about this one because... well, because you are making successive visits and possibly building up a case for settlement.

The next one is V 4.2 (d) will not undertake any prohibited activities set out in V 4.5 – V 4.10. It means you have probably built up some contacts in the UK where the likelihood of abuse is higher than the average visitor.

The other ones are in V 4.5 (a) and (b) taking employment in the UK; and doing work for an organisation or business in the UK. They will worry about these because these are the prima facie intentions for a former Academic Visitor to return to the UK sooner than the average tourist would.

All of these are reckoned by the Immigration Officer during your landing interview and his measurement is strongly influenced by your personal impact and articulation skills. Secondarily he will be influenced by your level of readiness to prove that you are a genuine visitor (having bank statements and employment contracts at hand, and so on). Your premise for visiting the UK so soon after a one-year visa will also be critically important. If you fail to convince the IO that you are a genuine visitor, you will be placed in custody and removed.

One option that some people opt for in order to mitigate the distress of removal at port and wasted airfares is to apply for entry clearance in advance. If you have been 'cleared' for entry, then the landing interview is reduced to a formality without the need for subjective judgements on the IO's part. For Americans, an entry clearance is optional, but something you might consider if your situation is borderline. Entry clearance applications for Americans are processed through the British Consulate General in NYC and cost GBP 83 (payable in USD). The turn-around time is about a week.