Keep in mind I am pretty new to this game. My favorite zone is probably the Conclave tests. I really got hooked on this game through the conclave tests. It's where I learned that there was more to the game than just randomly killing things. It made me get in the habit of slowly reading the descriptions, looking in every nook and cranny, and closing my eyes and really imagining the room in my mind. Maybe this zone isn't really that exciting for a veteran player, but to a noob with zero MUD experience, this is a beautiful zone. The only downside of course is that it is effectively a "single player" zone, which drops M in MUD.
My other favorite zone: Deep Mine. It is rich with stories, descriptions, and attitude. There is still so much there I don't know despite so many hours of exploring. Plus it is quite accessible to a novice player. Kagonesti/Dargonesti/Sahuagin are also nice though I am still exploring them. Of course I havent been to or soloed/lead many of the harder zones in the game (uth, hct, silvanesti, etc), so it's quite possible this list will eventually change!
Can't say I have a "favorite" solo fight ... anything that requires strategy, planning, thinking, and a healthy dose of risk is always fun.