Ok totally shameless plug but YOUR DIL yourdil.org is having a BBQ at the boston yatch club on July 15th (if you are around) [email protected] here's the contact email for details. There is the new ICA and the MFA (museums) Also walking around Newbury st (and shopping)

I don't know much about "must see", but if you want "must eat" places, check out:

1) The pescados (fish tacos) at El Pelon, on Peterborough near Fenway.
2) Okdul Bibimbap (korean rice hot pot dish) @ Super 88 or the Korean places at Union Sq.
3) This little sushi joint in Newbury St (sorry, can't remember the name).
4) Bartley's in Harvard Sq has great burgers (and a huge veggie burger selection).
5) Sweet potato fries at Bukowski's near Newbury.
6) Don't forget to hit ice-cream at JP Licks, Emack & Bolios, Toscanini's, and Christinas.

For touristy stuff there is the Duck Tours, the top of the Prudential, the Holocaust Memorial in Haymarket, and of course Salem MA for all witch stuff which is amazingly touristy and gaudy (hence it's awesome). July 4th there should be TONS of fireworks near the river. Check out the Aquarium & IMAX theater too.

Enjoy!