St. John's then ... or just outside Douglas. Not the airport itself at Ronaldsway as the station there is still open, though the second least used airport station in the UK▸ .
Ah yes - Ronaldsway International Airport station...
The reason for its lack of use is that the IOM Steam Railway doesn't advertise it as a call! It is a request stop for those "in the know" even though it is only 300 yards walk from the airport terminal building. When I was last on the island in 2017 I was staying at the Sefton Express Hotel which is even closer to the station, and got a remark from the guard when I asked him to stop three times on the same day!
The junction of the Isle of Man Railway and Manx Northern Railway a little west of St John's where the two lines diverge as they cross the River Neb.
The photograph is indeed of the twin bridges west of St Johns, where the Peel line (in the foreground) and the Ramsey line diverge. It was a much photographed location when the lines were open, because many trains were combined from Douglas to St Johns where the portions were split, and "races" often happened between the two drivers along here. The Peel train would have had the advantage of the gradient, but the Ramsey portions were usually lighter.
There was also a branch to Foxdale that once ran south from St Johns, and just east of the station that branch passed over the Douglas line. It is the only point on the Isle of Man where one railway is bridged by another.
As regards the day trip element, back in 2014 I found out that a small airline called Citywing were operating a twice daily service between Gloucester airport (Staverton) and Ronaldsway with an advertised flight time of 70 minutes. Leaving Gloucester at 0910 and Ronaldsway at 1710, it easily gave you six usable hours on the island. Regrettably Citywing went bust in 2017 (even more regrettably 4 days after I paid them £360 for two returns when we were going over for the Festival of Transport, but that's another matter...) and nobody else wanted the Gloucester route.
It is still possible to do a day trip to the Isle f Man today from Liverpool, Manchester or London City airports, but none of those is as convenient for me as Gloucester was. Easyjet fly to and from Bristol on Mondays and Fridays but only one trip on each day, so you can go from Bristol if you want a long weekend or most of a week on the Isle of Man (or longer periods of course).