While in Riga you should also go to
http://www.railwaymuseum.lv/ if you haven't already.
I am a big fan of Latvia in general, though more in relation to the country that it's railways. I was there a few weeks ago, and went to Jelgava.
I'm not sure what the best way to be polite about Jelgava is; it's a completely harmless town, and if you're purely interested in railways then it's not a bad place to go for that one thing, possibly the best outside Riga. It's just not particularly interesting in any other respect; the one saving grace for me was the boat trip on the river that wouldn't be running in winter. You'll have noticed that the service there isn't amazing; I took the train there and the really rather more practical bus back.
The station is big and busy with freight. The passenger side is a bit of a faded grandeur affair where the grandeur is almost completely faded, though there were a few really interesting historical boards up in the ticket hall. Until a few years ago there were a quite few random long distance services on lines that are now closed to passengers (
http://parovoz.com/maps/supermap/supermap-a.php?60,233 if you can work out where Jelgava is on the map; looks like EnrABA!), so the station layout reflects a concern with a lot more than a terminating EMU on one route.
I missed the opening hours of the Jelgava museum, though I must caution that it is quite small from the outside. It is the building in the first of my photos in
https://www.facebook.com/media/set/?set=a.10154422605565524.1073741858.891495523&type=1&l=eb6e5a37d7
What I would say is that I spent about 2 and a half hours there in the summer on a very nice day, and the only reason this wasn't too long is because it was the summer and I got a nice 45 min boat trip. I pride myself on in general only taking photos of nice things; so apart from the extreme roadworks photo I tried to make everything else in the album above look as nice as possible.
There are a number of nice buildings that the tourist information presents very well, like some churches among the soviet flats that if photographed from one spot look really nice. The palace is a bit of a let down, you can only see large amounts of it from the river, and if you get too close on land you worry about bits of it falling on you. If you have a wider interest in transport then there's a bus factory that I think you can visit (all the buses in Jelgava are split new lovely buses from it...).
The people were friendly enough, and young people seem to know English and be willing to assist you in interactions with older people that's second language is Russian. The two beggars that approached me in the street during the 1h45 mins I was there and not sitting on a boat also spoke English, but both quickly took no for an answer.
I think the place other than Jelgava that most meets your criteria for giving you a train journey and a place that's nice to see might be Tukums. Tukums has less trains than places on Jurmala like Dzintari, but the big attraction of Jurmala might mainly be the beach and so not so much in January. It's not a place of any railway interest though; a terminus of an erratic EMU service.
Sigulda and Cesis are really nice places, though from a railway point of view also not massively interesting at all, and are quite long journeys where you could well end up finding you wanted to take one of the more frequent coaches for one direction of the journey in order to get decent timings.
What you really need to see in Latvia is
http://www.banitis.lv/eng/index.htm, but it's a real mission to get to and I've no idea if it runs all year (I suspect it may not)! If you are quite mad, and willing to take the risk of getting stranded somewhere random if something is late, then you can do it as a 14 hour return day trip from Riga, but trains from Riga to Gulbene only run one or two days a week.
The train timetable at
http://www.1188.lv/transport/train is quite user-friendly, and if you find that you need buses for a return journey the timetable is at
http://www.autoosta.lv/?lang=en
If you like (ie PM me so I notice...) I can probably scan some of the tourist information for any town you might be interested in.
