1.     I would suggest not to drive from Tallinn directly to Tartu, but take a detour and admire Shore of Peipsi Lake.
Tallinn – Rakvere (99 km / 1h 12 min)- Kuremäe ( from Rakvere 91 km/ 1h 10 min)- driving along lake Peipsi (Lohusuu, Mustvee, Alatskivi)  94,6 km/ 1 h) to Tartu (from Alatskivi 40 km/ 37 min)

• Rakvere visit 13th-century castle ruins, open 10-18, ticket 9 euro
• Kuremäe
  The Pühtitsa Dormition Convent (Kuremäe Convent) is open every day: 07:00 – 19:00, free
• Mustvee
  Mustvee Old Believer’s Museum is one of the 21 places in Southern Estonia worth discovering that are marked by a yellow National Geographic window; is open advance bookings only
• Alatskivi
  Alatskivi Castle is a Neo-Gothic castle in Alatskivi, Estonia. Dating to the 17th century; amazing rose garden. Take a tour in the castle, participate in workshops
• Have dinner in Alatskivi pub or
• Fish and Onion Restaurant of the Old-Believers of Kolkja open 12-18
• And/ or visit Peipsimaa külastuskeskus /Peipsimaa Visitor Centre. Workshops, dinner, info…open Wednesday- Sunday 11-18
  

2.     From Tartu
Vastseliina 99 km/ 1 h 16 min– Kolodavitsa ( 19,5 km/ 20 min) – Piusa (4 km/ 5 min) – Orava (8 km/ 10 min)- Värska (16,6 km/ 20 min) – Taevaskoja (49 km/ 40 min)- Tartu  (48 km/ 38 min)

• Vastseliina Episcopal Castle was built in 1342 on the lands of the Bishop of Tartu and it became one of the most powerful fortifications in old Livonia
• The Piusa sandstone caves, Ticket 5 eur
• Bread baking workshop in Obinitsa, 15 eur, advance bookings only
• Värska
  Beautiful lake and amazing nature. Pick and eat wild blueberries and lingonberry.
  Word-famous Värska mineral water.
  Be careful.:) This is the area of States Borders. Be careful and follow signs. Latvia is in EU and you welcome to visit Latvia, but for Russia, you need a visa J
  Have a dinner Seto Talumuuseumi Tsäimaja in the Seto Farm Museum. 
• Taevaskoja sandstone cliff. Very beautiful. Have just for a walk or ask for a guided tour. Check from this link for other activities.

3. Tartu- Võru ( 71 km / 56 min) Munamäe (10 km/ 14 min )  Rõuge ( 15 km/ 15 min) Sangaste loss ( 70 km/ 1 h)  Pühajärve ( 22 km/ 20 min)  Tartu (48, 5 km/ 40 min)
   

• Võru
  beautiful lakes, promenades;
  Võrumaa Food Center (the title of the “Year of the Woodwork” awarded to the building), a monument to the “Estonian Food”, which was erected by a farmer from a private person and paid the price of a combine.
  Find Piret Pilberg linen fashions Võru, Tartu 31
  Admire painted flats houses in Võru, painted by Navitrolla
• Suur Munamägi Observation Tower
  The highest peak in Estonia (and the Baltic states), reaching 318 meters (1,043 ft) above sea level. Suur Munamägi (translation is” Big Egg Mountain”)
  Ticket 4 eur
• Rõuge Suurjärv
  Lake Suurjärv in Rõuge is the deepest of the Estonian lakes – 38 m. There is a public sandy beach near the lake and the hiking trail in the Rõuge Primeval Valleyruns along its shore.
  The Monument to the Estonian Mother
• Sangaste Castle
  The castle was built earl Bergs, rye breeder – “Estonian rye King” Castle in the Vinzor style,
• Pühajärve and Otepää
  Pühajärv (“Holy Lake”) is a lake in Estonia, near the town of Otepää. Otepää is the most well-known winter sports centre in the Baltics and the Winter Capital of Estonia. Otepää got its name, which in Estonian means “bear’s head” after the shape of the castle hill. Otepää is first and foremost known as a ski resort and here you can enjoy cross-country and downhill skiing, as well as snowboarding and snow tubing. During the summer you can hike along the paths of Otepää Nature Park,
  Have dinner in Pühajärve SPA or in a very fancy restaurant GMP Pühajärve.

4. From Tartu to Viljandi (75 km/ 58 min) Riidaja ( 45 km/ 39 min) Helme (10,8 km/ 10 min) Taagepera (15,6 km/ 13 min)  Lilli ( 10 km/ 18 min)  Tartu (96 km/ 1h 30 min)

• Viljandi
  My childhood hometown
  impressive castle ruins, former home of the ruling Livonian Order. Two lakes, The Kondas centre of naive art; Estonian Traditional Music Center.

Park your car near the bus station/Centrum. Walkthrough Tartu Street to Castle ruins, Go down the Trepimägi to the lakes of Viljandi
Rent a boat.
Go back to the old city, visit recycling fashions stores (there are a lot of and very good ones)
Have dinner in Roheline Maja or Fellin or Amrita Pizza.
Rent a bike: Joosepi Jalgrattapood Kaalu 9, Viljandi

• Riidaja
  Bagpipe Holiday House. You can enjoy the performances of Anu and Triinu Taul. The farm has its own airport. Sightseeing flights with a motorized hang glider.
• Helme Caves and manor
  Situated to the north of castle ruins, the caves have a white Burtniek layer of sandstone walls standing 3 m high
• Taagepera Castle
  is open advance bookings only. Baron Hugo von Stryk had the impressive art nouveau castle built as a home for himself more than a hundred years ago.
• Lilli
  Teringi study trail 4,5 km . Go hiking!! J Perfect overview of Estonian bogs. If you are brave enough, you can swim in a bog- lake J
  Your biggest problem can be mosquitos (depending on weather). Buy some repellent.