A couple of comments, mainly aimed at railway interest. Denmark does not have much in the way of spectacular scenery, although there are plenty of pleasant bits of coastline or rolling/wooded landscape.
It used to be possible to buy Øresund Rundt tickets that would allow you to make (over two days) a loop Copenhagen-Malmö-Helsingborg-Helsingør-Copenhagen in either direction starting anywhere you wanted and with side trips. I think this ticket is now more difficult to find: possibly only on line or from the Copenhagen Tourist Office. If you do travel there is Stenvalls Transport bookshop near Trianglen station in Malmö.
(More to come.)
With regards to the comment above on the Øresund Rundt ticket, if your Interrail pass covers only Denmark and you want to see more than just Malmö, it is probably cheaper than buying the Swedish section and the Helsingør-Helsingborg ferry separately. It might even include a free coffee and cake on the ferry: it used to.
From Copenhagen you could try going to Nykøbing F. There are three routes: the traditional route via Roskilde and Ringsted to Næstved, the new route to Ringsted and then Næstved, or via S-Tog to Køge and then Næstved on a local.
If visiting the museum at Odense you could take a side-trip to Svendborg. You could even take the ferry on to Ærøskøbing, but no longer on the train-ferry Ærøsund: they sank it.
There is some stabling on the east side of Østerport station and at Helgoland, which is between the 25 kV Lines east of Svanemøllen S-Tog station. Other stabling is on the approaches to Copenhagen H.
To pass the depot, leave the S-Tog at Dybbølsbro station and turn left (or walk there), turn right at the end and follow the fence. Where the road splits at the end of the depot building, veer right and follow along. On one side is the old main works and near the end are small cottages that were inhabited by works employees, particularly those who were in the breakdown train crew. There should still be a tunnel at end of the road: at the far end you can turn left and walk to Sydhavn S-Tog station. You can either come back to the city and see the area from the other side or go on to Ny Ellebjerg.
I must make it clear that have not been able to get to Copenhagen for four or five years.