One cheap way to get to Tokyo is the りんかいフリーきっぷ (Rinkai Furii Kippu). It allows a trip down to Tokyo, unlimited travel in the city, and a trip back. It lasts for two days. See the JR East Website
You can buy the ticket from the major JR stations in Gunma (Takasaki, Maebashi, Shibukawa, Numata) from the machines. The price may change based on how far away you are, but it seems that most of Gunma runs 3,790. For the math savvy, that works out to just 10 yen more than a roundtrip ticket. If you're just going to Tokyo overnight, in almost all cases it's worth the extra 10 yen.
If your machine has an English button, hit that... the ticket is sold under the "discount tickets" section. If not, "discount tickets" is the 2nd button up from the bottom on the far left.
You will receive three tickets. One is used to travel from your originating city to Tokyo. It has the kanji for your starting station with an arrow after it. When you arrive in Tokyo, the machine takes your ticket and you start to use the second ticket. You can travel all over Tokyo with it – generally within a few stops outside of the Yamanote Line – and use it to return home. The third ticket is information in Japanese. You can throw away that one, but make sure you aren't throwing away the tickets you actually need.
Additionally, if you're a bit more high class, there is a Shinkansen version of this ticket as well. It runs at 8,590.
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