I debated whether or not to visit, but in the end, I wound up taking the two hour train ride to Hakone (Kanagawa Prefecture).
Along with Nikko, Hakone is one of the most popular destinations for Japanese and international tourists looking to escape the hustle and bustle of Tokyo. The area is famous for its onsen (hot spring) resorts and majestic views of Mt. Fuji.
The Odakyu Railway Company runs a wonderful deal. For under $50 USD, one can buy a two-day unlimited "Hakone Free Pass", which grants unlimited usage of Hakone's many transportation systems (railway, bus, sightseeing ship, cable car). The round-trip train fare from Tokyo to Hakone is also included in the price of the pass.
With the Free Pass, I was "free" to leisurely explore Hakone. The primary sightseeing route is basically one giant loop that starts and ends at Hakone Station. The course includes a boat ride across Lake Ashi, a cable car ride into the volcanic Owakudani valley, and a train ride back through the mountains.
Hakone is renowned for its beauty, and indeed, the town is quite beautiful. I imagine that Lake Ashi in particular is breathtaking when all the autumn leaves change. However, visitors should be forewarned that views of Mt. Fuji can be elusive, even with clear skies.
There's not much to do in Hakone other than admire the natural beauty and visit an onsen (I did both). Many tourists choose to spend a night in a ryokan, but I found Hakone to be a perfectly manageable day-trip.