What exactly do you consider to be "moving off home base"? Does that just mean trips or activities that take you away from San Jose overnight or does that also include ANYthing that takes you away from your primary focus of mongering for more than just a couple of hours? There have been PLENTY of posts concerning DAY trips in around the SJ area. Here is just 1 post by me that lists over 50 things you can do
http://www.costaricaticas.com/phpBB2/viewtopic.php?t=16082&postdays=0&postorder=asc&start=16. Some of those activities can be done in just an hour or two, squeezed in between MP visits. Most of them, however, will take at least a half a day or more, and a few will take as much as 10-11 hours from the time you leave your hotel to the time you get back and can start mongering again. Obviously, it doesn't take nearly that much time to recharge our batteries and if you go with some of those you will probably forego at least some of the mongering you might otherwise have been able to do (e.g. only 2-3 sessions per day instead of 3-4 or 5). However, for most guys that still leaves PLENTY of time each day for mongering and these day-trips can really add an important non-mongering dimension to their trips.
The other question I have about your post is whether you're mostly asking about fun activities to do while you're recharging in general with perhaps the opportunity to enjoy a little sun as an added bonus or more specifically JUST those activities that give you an opportunity to do some serious sunbathing. If its the latter, you should be able to get some sun on most of the activities that are normally discussed on this board(museum-going being the notable exception, and the one perhaps best saved just for rainy afternoons). However, one should keep in mind 2 things. Because of SJ's altitude and southern latitude, the sun may be a lot stronger than the one you're more used to at home and you could indeed get a lot of color just walking around because of that. OTOH, I don't really recommend walking around SJ in shorts, let alone with your shirt off, and so most of the color will go solely to your face and perhaps arms rather than your back, chest and legs (hence the red faces of some mongers). So, I wouldn't really consider that to be real "sun-bathing". You probably won't get a lot of sun aboard a bus out to Cartago either, but that doesn't mean it wouldn't be a worthy trip for all the other reasons discussed. If you go to the top of one of the nearby volcanos (an excellent half day activity) the sun will be stronger still but, also because of the even higher altitude, it can be QUITE cool and you'd be even less likely to have much of your skin exposed. In fact, a visit to the top of the Irazu volcano followed by a stop by the Basilica in Cartago (already discussed) on the way back to SJ would make for an excellent combo. You'll probably want to leave early in the morning for this (no later than 8AM, ie much before any mongering opportunities really get going in SJ anyway) so you can get to the volcano before it starts to cloud up and even with a stop-over at the Basilica in Cartago you should be able to back in SJ by around lunchtime which isn't until many of the MP girls start showing up any way.
Unfortunately some of the best activities for more full sun exposure are also the more full day activities. For example, while not really a sunbathing activity, going on a rafting trip means wearing swimming trunks and often getting a lot of reflective sun off the water, so it is not at all unusual to return from a day of that with a lot of red skin (especially on the tops of your feet and thighs in addition to your face and arms, while your chest and back will still be pretty well protected by your life-jacket). The "problem" with this is that you usually don't get back to SJ from rafting until late afternoon and so probably won't be able to get in even 1 daytime MP session. Another GREAT day trip, that IS arguably primarily a sunbathing activity, is the Calypso Tortuga Island Cruise, which takes you down to the coast, out on a catamarran and over to an island where you can lay on the beach for a few hours before returning in the early evening back to SJ. That combination of sea, sun and sand can result in a LOT red skin. Unfortunately, this trip returns to SJ even later than the w/w rafting trips, so again any daytime MP sessions will be pretty much ruled out on the day of that trip as well.
Frankly, I'd be more concerned about using enough sunscreen so that you don't wind up with one of those red faces and getting too much sun from just doing your usual day-to-day activities, then in going out of your way to do any real sunbathing.