The Dungeon main wall is mostly all 12- and more difficult. The harder routes are really quite fun and stay shaded most all day. That said, there are a couple of 5.10s on that side of the small canyon. The north side has shorter, easier routes that are popular with locals but I'm not sure they're worth traveling to specifically. If you'll be in the Los Alamos area already, it's definitely worth a visit but if you're not interested in the 5.12 climbing, I wouldn't recommend it as a travel destination.
If you're interested in sport climbing in the Los Alamos area, I'd recommend Upper East Fork (UEF), Las Conchas or Area 37 on account of the much larger variety of climbing. These areas are a twenty minute drive from Los Alamos.