Esja is north of the city across the bay; it looms a bit like Rainier over Seattle, although it isn't nearly as high. It's easily reachable by bus, although I had some bus misadventures I won't detail here. The 57 bus from the city stops right at the trailhead, and the fare is very reasonable.
(Apologies for the lack of photos. My phone and Blogger aren't playing well together.)
It's a beautiful hike. While it's volcanic, it reminded me more of Colorado hiking. At lower elevations there were many flowers, including the ever-present (invasive) lupin, as well as babbling streams. The trail itself is steep, but wide and smooth.
There are two routes up, as well as a path that doesn't go up to the top. Both of the routes up get increasingly steep and meet shortly before Steinn, a boulder with a register. Many people turn around here.
I kept going; the steepness increases sharply, and I certainly felt it. Up ahead I could see the rocky, fluffy cap, which was nearly vertical. At one point I made a wrong turn and found myself less than 20 feet from the cap but with no way to reach it - the surface between me and it was loose, steep, very exported dirt. I was heading back down when I found the actual trail and proceeded up again.
The cap involves rock scrambling. In many places chains are anchored as handholds. It's not exceedingly difficult climbing, but the exposure is a bit unnerving.
However, I did make it to the top, the Þverfellshorn, and signed the register. From there, the mountain continues as a long ridge, reaching the true peak at a further point.
The hike is 2.8 km one-way with 545 meters of elevation gain or so.