If you have plenty of time to explore around Hamamatsu area, please check Hamamatsu/Hamana-Lake Daisuki (meaning “Loving”) Net for the tourism information. The site will tell you how many options you can have... Also, the site is beautiful, at which is just worthwhile taking a look.
Following are the several recommendations when you have not much time that can be spent in Hamamatsu area;

• Hamamatsu-City Music Instrument Museum
  Hamamatsu is known for the city of music due to wonderful piano makers such as Yamaha. Over 1,300 music instruments are collected over the world and exhibited in the museum. You can see them around and you can touch and play some of them. 
  https://gakkihaku.jp/en/
• Observation Gallery at the 46^th floor of Act Tower
  Act tower is the highest building in Hamamatsu and the surrounding area. You can go up to the 45^th flor and see around the area. 
  https://act-okura.co.jp/facilities/gallery/ (Japanese only)
• Hamamatsu Castle
  Edo Era was begun by Ieyasu Tokugawa and he stayed at Hamamatsu Castle over 17 years. This is the reason that the castle is known for “advancement for one’s career.”
• YAMAHA INNOVATION ROAD
  Yamaha is one of the world-known companies of which headquarter is located in Hamamatsu. This gallery was newly opened last year to exhibit the company’s history and their ideas for the future. The place is very chic and has been popular. Reservation is needed although it is free to visit. Open only on weekdays.
  https://www.yamaha.com/ja/about/innovation/ (Japanese only)

A little bit far...eding a half day or more though, there are a few recommendations;

• Nakatahjima dune
  This due is located in Enshu-Beach with 600m of north-south and 4km of east-west widths. The view is spectacular but be careful of the strong wind and be prepared for getting a lot of sand on your heads and in shoes. But it is worthwhile. You can take buses from Hamamatsu station to get there.
• Hamamatsu Flower park
  It exhibits many kinds of flowers collected from all over the world.  You can see seasonal flowers. You can get there by taking the busses from Hamamatsu station.
  https://www.e-flowerpark.com (Japanese only)