The Palace of Amber should be a nexus for RP, especially political stuff. A lot of interesting direction-changes take place when people bounce off each other in court, and giving yourself the chance to do that is rewarding. Take a look at
http://wiki.roadtoamber.com/amber-palace if you're unsure as to why you might be in the Palace, but here are a few ideas.
* Going to get the gen. Picking up the gossip so you can tell other people.
* Going to find people to persuade of your point of view. If you have something to say, then saying it in the palace, where you are likely to be able to use social and people gifts, is a good thing. Persuading the NPCs present can sway PCs too.
* Going for company. The social life of Amber, the Ton, gathers here. If you know anyone in Amber, you probably have NPC friends who are happy to show off to you. If not, then it's perfectly allowable to try to make those friends. NPCs are not the heros of the story, but they are a very handy hook.
* Trying to find someone and failing. Looking for Prince Caine, to offer him your latest deal? You can still talk to Gerard, and the drinks are likely to be better. The Great Houses all have suites in the Palace - you can fail to find them there.
Some of these reasons also work elsewhere, but the long and short of it is, the palace is a public place for place. Feel free to be there, and handwave the reasons.