I'm not an Estonian, but I have spent a little bit of time there. I don't know if you might be too ambitious to plan to see Tartu, Tallinn and Saaremaa in 2-3 days. From what I know about the islands, they are more a place to relax for a few days rather than investigate in a single day. I wonder what Loiks thinks?
As for Tallinn and Tartu, I'll repeat the advice that I gave to Saar before he went there:
Tallinn's old town is really quaint (though quite touristy). Lots of expensive little souvenir shops to wander around. There's the Occupation Museum too, which is worth a visit if you're interested in history; an impressive nightlife. Just outside the centre, I thought the Kadriorg Palace was very nice and there are reasonable beaches at Pirita. You can hire a bike to cycle around.
Tartu could be an overnight stop, it's the university city, very authentically Estonian and quite pretty, with its own 'leaning tower'. It is home to the excellent Museum of National History, again good if you're interested in history.
Narva is a depressed Soviet town just shy of the Russian border with one redeeming feature: there are two castles within a stone's throw of each other, one on the Russian side, one on the Estonian side. They are quite magnificent, and the stream marking the boundary between Estonia and Russia is deeply symbolic... I really liked this place, but there's really nothing else to see in Narva and it is quite far from Tallinn.
Parnu is a pleasant, quiet resort town on the West Coast, where you can have a mudbath. Again, though, it's probably not worthwhile if you're only going for a couple of days.
is a great site for exploring the options for tourism in Estonia.