Lords of Waterdeep is very similar to Stone Age, just with some hidden information added and dice removed. I haven't played with any of the dlc packs, so can't really comment on them.
As for other iOS board games, I do recommend Carcasonne highly. Ascension is technically a card game and not a board game but is a pretty good design and can be played over and over mixing and matching expansions and new strategies and such for infinite replay value. And then there's Fortune Street, if you've never played a version of the squeenix gem yet and want to know how a well-designed Monopoly would play out.
If you are interested in a card/board game that has an actual populated online lobby I highly suggest and will always suggest Spectromancer, which is also on Steam. Spectromancer was originally created about twenty years ago by Richard Garfield, fresh off his successful sale of Magic: The Gathering to Hasbro. Spectromancer has a similar conceptual design to Magic and the ties to Garfield are readily apparent, but the twist is that rather than pre-build a deck of cards, you pick a class and are given a 'hand' of twenty randomly selected cards from the game's pool, which are not spent when used but are hidden information until your opponent sees you play it. This means that while the game's setup is semi-random, the game itself plays very chess-like. There are no drawing new cards as the game progresses and as a result you're very capable of planning several moves in advance. The only hidden information is what cards your opponent has yet to play, and even that can be deduced because the opponent's 'hidden' hand is still sorted by color/cost, and certain things like how they choose to spend their resources of each color tells you which they'll build up for and which they want to have on hand, that sort of thing. And if random starts aren't your jam, there are extra modes for draft and constructed play as well, not to mention a long-ish single player campaign with a plethora of Hearthstone Tavern Brawl-like scenarios that mix up the standard formula.
