Formal/Condescending:
* Condescend
* Stoop
* Grace (as in "grace me with your presence")
* Favor
* Patronize
* Bother
* Think fit
* See fit
* Vouchsafe
Neutral:
* Agree
* Accept
* Permit
* Allow
* Grant
Informal/Negative:
* Lower oneself
* Humiliate oneself
* Deem oneself worthy
The best synonym will depend on the specific nuance you want to convey.
For example, if you want to emphasize the condescending nature of the action, "condescend" or "stoop" would be good choices. If you want to simply express a willingness to do something, "agree" or "accept" might be more appropriate.