You didn't mention exactly which property , so it is hard to answer this.

You can have flowers sent to the room from a florist. If you can, I would suggest checking in earlier in the day and getting the room ready, when the two of you enter the room later, it will be a surprise, but I know this isn't always possible. Most full service Hyatts allow you to chose some options such as flowers from Hyatt E-Concierge before you check in, but don't expect it to be cheap.

My only personal experience is that Park Hyatt Tokyo will give you a small flower bunch for an anniversary or birthday. I have also read that hotels some do give upgrades for special occasions, but that is up to the staff. Emailing or adding a mention in the special instructions when you book wouldn't hurt.