I went to the Topkapi Palace today. Although some individual rooms of the harem were closed off, there were many more to explore; I do recommend the harem. I'd say the Topkapi is open for business. It is large; I spent almost six hours there, though well over 30 minutes of that was in the ticket line, the audioguide line and the museum entry line. The line for the museum varies, so you might check it out when you arrive and see whether it looks like a good time to tackle it.
You have to leave an ID if you want the (free) audioguide. Be sure they give you a claim ticket so you don't have a problem retrieving your ID at the end of the day.
I was disappointed by Aya Irina (Hagia Irene), which is included on the Topkapi combo ticket. Much of it is blocked off, one assumes for restoration, but there don't seem to be any interior decorative elements (no tile, mosaics, carfed wood, etc.), so I'm not sure it's going to be an exciting option even when it's reconstructed. Let's just say it's a poor substitute for the Chora Church (now Kariye Mosque), though I'm sure it's of interest to those into early church architecture.