From Narita Airport, Takasaki is served by Azalea Limousine Buses operated by Chiba Kotsu; buses leave once every 1 1/2-2 hours (3 hours to/from Takasaki Station, ¥4500). By train, the easiest (and most expensive) way to reach Maebashi is to take the Narita Express to Tokyo Station, then the Joetsu Shinkansen to Takasaki (Approx. 2 1/4 hours, ¥7800, no charge with the Japan Rail Pass or JR East Pass). Reservations for the Narita Express and Shinkansen can all be made from Narita Airport.
From Haneda Airport, Limousine buses operate to/from Takasaki Station (3 hours, ¥3500). Going by train is much faster, but more expensive and requires more transfers: The Keikyu Line to Shinagawa, the Yamanote Line to Tokyo, and the Shinkansen to Takasaki (Approx. 1 3/4 hours, ¥5200; cheaper with unreserved shinkansen seat). You can purchase tickets for the JR portion of the journey upon reaching Shinagawa.
Takasaki is a stop on the Joetsu Shinkansen and Nagano Shinkansen lines, and is a hub for the JR Takasaki, Hachiko, Ryomo, Joetsu and Shin-etsu lines.
Frequent Shinkansen services depart Tokyo station for Takasaki every 15-30 minutes, with more frequent departures for the evening rush. You can reach Takasaki in about one hour, at a cost of ¥4800. Regular trains on the Takasaki Line depart from Ueno station 2-3 times per hour, reaching Takasaki in about 2 hours at a cost of ¥1890.
There are also hourly departures for Takasaki on the Shonan-Shinjuku Line which runs via Shinjuku station (1 3/4 - 2 hours, ¥1890 from Shinjuku).
Nippon Chuo Bus operates several daytime bus services from the Tokyo area to Takasaki. All buses stop at the Hilton Tokyo in Shinjuku, with some buses also stopping in Ikebukuro and Akihabara (2 1/4 hours to/from Shinjuku, ¥1500).
Other long distance buses include the Tokai Liner daytime runs from Shizuoka and Nagoya, Sendai Liner overnight runs from Sendai, and Silk Liner overnight runs from Nara, Kyoto and Osaka. All of these buses are operated by Nippon Chuo Bus.
The city centre is easily walkable, but to get to most of the sites, bus, bicycle, or car are needed.
Buses are usually infrequent and there is no English information. Ask the tourist information board at the train station for information on bus times.
Mt. Kannonyama and the enormous statue on top of it are the most obvious attractions. You can enter the statue for ¥200 to get a good view of the city from the top. Halfway down the mountain there is a cave with Kannon sculptures carved from the stone inside, along with a Japanese garden. Entrance ¥800. To get there, you can catch a bus from Takasaki Station, although they're infrequent, and it might be more interesting to walk up Kannon-dori and up the (long!) stairs to the top of the mountain.
Shorinzan Daruma Temple is famous for being the place where daruma dolls originated. The temple itself is nice, although nothing too special. The small museum of old daruma dolls beside the main temple is interesting.
About 8km from the station is a collection of ancient keyhole tombs ('Zenpou-Kouen-Fun') along with an archeology museum (and a literature museum, probably of negligible interest). The tombs are roughly 1500 years old and in a distinctive 'keyhole' shape. One has been restored to look as it would have 1500 years ago, complete with haniwa clay figures and pots. English information is good and plentiful.
Gunma no Mori (群馬の森) is a forested park around 9km from the station. The Gunma prefectural museum of art and the prefectural museum of history are both located inside. The buildings are both notable for their architecture.
Mt. Haruna is a large dormant volcano within Takasaki. By bus from the station it takes about an hour to reach the top. The shrine was founded in 586 and is very scenically located on the side of the mountain beside a river. Lake Haruna is a large crater lake a bit further up with various tourist facilities. It's possible to walk between the two, but the path is fairly long and poorly maintained. Buses come only every hour though, so it may be worth it.
The ruins of Minowa castle are in the town of Misato, near the base of Mt. Haruna. There isn't much left to see, but with the help of a good imagination and artist impression, you can get an impression of what was once an important castle. Except for the well and a few rock walls, there are almost no parts of the buildings left, but the earthworks and moats are all visible. All signs are in Japanese and there are some photos from excavation work showing many details that have now been grown over. More interesting as a place to walk around in a forest than for historical or cultural reasons.
Daruma dolls are the local specialty. The omiage shop at the train station sells them in small sizes and in all colours. Or you can go to the daruma temple and buy them in all sizes (and they can get quite big), although only in red.
Shoya (庄や), Yajima-cho 117-8 (on the ground level on the left side of the plaza at the West Exit of JR Takasaki station), tel. 027-328-8833, . Open daily 11:00 am to 7:00 pm, Sundays and holidays 1:00 to 5:00 pm. If you can tolerate occasional smokers, this is a pleasant place to sample a wide variety of specialty snacks and sake from around Japan while you wait for train connections. Its catch phrase is kutsurogi no sato 'a place to relax' and the happi coats of the staff say yorokonde 'enjoy'. Not much English spoken, but there are picture menus  for both food and sake. Snacks range in price from ¥300 for edamame (soybeans) or kimchee to ¥1300 for a serving of shabushabu, with most in the ¥500 to ¥700 range. Overflowing glasses of sake in masu (square boxes) run about ¥700-800.
Yaki-manju is a Japanese sweet famous in Gumma. It's broiled manju, Japanese-style bun with sweet soybean sauce. You can buy one at any shop with a long line of customers.
Ashikaga - historical home of the Ashikaga shoguns
Karuizawa - a popular winter and summer getaway with skiing and shopping - a traditional shopping street as well as a huge outlet mall with a number of Western brand stores. One stop westbound from Takasaki on the Shinkansen. For a slightly less expensive route take the Shin-etsu Line west to Yokogawa Station in Annaka and take a 30-minute bus ride through the hills to Karuizawa Station. Savings aside, the bus is worth the extra time during autumn for the colorful scenery.