My experience as an adventure game player goes way back to the text-only Colossal Cave game, which then morphed into the classic Zork text games from Infocom (which, by the way, you can play even now on iOS with the Lost Treasures of Infocom app).
Now, with speed and graphic power, games are a lot more immersive and fun to play. Tipping Point Adventure, is a recent iPad-only release that is rich in puzzles and high quality graphics. The game is currently on sale for U.S. $1.99 in the app store. You begin the game sitting in your virtual home watching TV, when a strange message sets you off on an epic adventure. At first, I was stabbing around the screen looking for things to interact with, but soon I saw a logic to the way the game was constructed. I liked a lot of the subtle things the author has done, like picking up the TV remote and selecting stations has old movies actually playing on the TV. The game has built-in hints available but there is no in-app purchase required to get them, so unlike some other games, you don't have to buy them. I still needed one or two of the built-in hints. One hint told me I had to go to a particular TV channel for a message, and with hundreds of channels available, I don't think I would have figured that one out for myself.