When did the eruption begin date wise? Where would you recommend we visit in Iceland?
It depends on how much time you have. Many attractive places are in the vicinity of the capital Reykjavík (we are far from beeing affected by this all), and most take the so called golden circle, that takes in the most popular and known places:
http://en.wikipedia.org/wiki/Golden_Circle_(Iceland)
If you have more time, it is nice to linger a bit in the countryside, f.e. go to the North, and visit Akureyri, Mývatn and Húsavík, which has a very popular whale watching operations. You can also see that in Reykjavík, and not so far from Reykjavík you can also see the whaling stations, which is thankfully now back in bussiness.
As the volcanic eruption is probably over in the summer, or at least managable, the southern part will be quite safe to visit, and of course the highlands are popular, Landmannalaugar and Thorsmörk could be open although it is closed now due to its vicinity to the site.
Then you could also go to the Vestmann islands, or even to the Vestfjords, which are off the beaten track but very nice. If you like hiking we have lot of routes, short and long, one of the most popular one walks between Eyjafjallajökull and Mýrdalsjökull where Katla is, and the path is just by where the eruption started, before it moved under the glacier. It is called Fimmvörðuháls:
http://en.wikipedia.org/wiki/Fimmv%C3%B6r%C3%B0uh%C3%A1ls
It started eruption there on the 20. of march, then a little lull came in it and few days later it came out under the glacier itself, few kilometers away.
Have a nice time, and take care to prepare for fantastic summernights where the darkness never comes.