Tunnel 3 (the one on the right as you enter the main room) is the most interesting at this stage of the game.
In the first room, look at the left wall to see a puzzle with scarabs on it. One of the scarabs is missing, so there's nothing to do with it till you find that last scarab, which will happen sometime after you find the burial chamber.
The next section of tunnel 3 is a very large room with an uneven floor that looks like it ought to have all sorts of fascinating stuff -- but there's nothing here. Pass on through to the next section.
In the next room, look at the wall on the left to find a puzzle Nancy refers to as the Queen's Tiles. (She says they're mentioned in Jon's notes, and they are, on the last page; but he doesn't use that title.) Finally, a puzzle without any missing pieces!