Irazu IS a good day trip
IF you combine it with visits to other attractions east of SJ, such as Cartago, Lankester Gardens, the Orosi Valley, etc. But I seriously doubt anyone would want to spend the whole day just at the top of that volcano. Besides, he wasn't just looking for day trip recommendations, a topic that has been covered many times already, but rather for day trip recommendations out of SJ
AFTER 9AM. I doubt there are many Irazu tours that leave after 9 and if there were they wouldn't get there until after 10AM, which is often when the clouds start to move in for the day to obscure the views.
Arenal would be a good day AND evening trip and an excellent capper to your trip, but it is one long-ass day. It takes 3 hours to get there and another 3 hours to get back so, even with an 11 or 12 hour trip, you'd be spending half your time on the road (not that that is such a bad thing given the wonderful scenery along the way). I'm not so sure there are actually any "afternoon" trips since the whole thing is so long to begin with, but there are some tour operators which offer that tour with midmorning departures from SJ. So that might qualify for what TXS is looking for.
Personally, I think Arenal deserves much more than a rushed day visit, but if you're one of those mongers who just can't stand that the thought of spending even 1 night outside of SJ (or perhaps Jaco) with all their mongering opportunities, then I guess 1 day (and evening) is better than nothing. OTOH, since you're not leaving until 3 the next day, if you don't mind foregoing the mongering for your last night OR if you're prepared to bring some "companionship" along with you to Arenal (which might be the best option of all), then IMHO an overnight to Arenal would be a much better way to go.
For day trips out of SJ that are more geared for just day trips and which leave after 9AM, I do have some other suggestions.
1) La Paz Waterfall Park
http://www.waterfallgardens.com/lapaz-waterfallgardenspark.html has tour packages with hotel pickup in SJ between 10-11AM. They also return around 4PM leaving plenty of time for a last night of mongering or even an afternoon MP session.
2) Paraiso ATV tour
http://www.paraisocostarica.com their morning tour leaves at 8AM and returns at 1PM, which rules that out, but they also have an afternoon tour that leaves at 1PM and returns at 5PM, PLUS they are a CRT sponsor and offer a discount if you are a VIP member.
3) Cafe Britt
http://www.cafebritt.com/CoffeeTour/index.cfm has regularly scheduled tour pickups at various downtown SJ hotels between 9:30-10:30 for their 11AM tour and between 1:30-2:30PM for their 4 PM
4) The Butterfly Farm
http://www.butterflyfarm.co.cr/tbf/index.htm is probably best packaged with other tours such as with Cafe Britt but can also be done as a stand-alone. It has shuttles that pick people up downtown at 10AM and 2 PM.
5) These are just the tours that I
KNOW offer pick-ups after 9AM. I'm sure there are others. It is also possible to contact some of the other various tours to see if they offer (or can arrange for a fee) later pick-up times. For example The
ORIGINAL CANOPY TOUR at Mahogany Park
http://www.canopytour.com/mahogany.html is located about 1.5 hours from SJ. Normally, they pick up in SJ around 8AM (presumably for their 10AM tour), but they also have zip-line tours that don't start until noon and 2:30PM and according to their website "can pick you up at hotels in San Jose... for a nominal fee" (whatever that means)
6) Even if they don't mention pickup in SJ, it is also always possible to arrange the transportation on your own. For example, Turu Bari Park
http://www.turubari.com is within a reasonable (1.5hr) distance of SJ and has all sorts of activities and attractions that can be enjoyed throughout the day... once you get there. Colinas del Poas
http://www.colinasdelpoas.com/ingles/canopy.htm offers another canopy tour up in the mountains (actually on the way to Poas) that is less than an hour from SJ and has canopy tours that start at 11AM and 2PM.
7) Finally, if none of these interest you or you don't want to spring for a private driver, etc., there are also SOME things of interest right in SJ itself that won't cost you an arm and a leg. The National Museum is good for a couple of hours by itself and there are other museums downtown as well. Admittedly this is not the most exciting way to end your trip but does leave you plenty of time for doing the always reliable "MP walking tour" that has already been suggested.