My suggestion would be:
Day 1 : Pairi Daiza
Day 2 : Frankfurt. Keep in mind that the zoo is situated within the Umwelt-zone with restricted access for vehicles (you'll need a permit). You can take the 661 highway, exit 8, crossing the railway heading to the Eintracht Frankfurt football stadium, park nearby and take the underground U7 at the Johanna Tesch Platz or the Gewinnerstrasse underground stations. Afterwards you have excellent acces to the A3 Nurnberg-Plzen or the A5 Heidelberg-Karlruhe-Stuttgart
(extra) Day 3 if you heading to Stuttgart: Heidelberg Zoo and Karlsruhe Zoo are easy to combine. Stay in Heidelberg and enjoy the historic old town. The zoo is outside the Umweltzone in Heidelberg, and within (but at the edge) in Karlsruhe. Both are pleasant zoos with varied collections.
Day 4 : Stuttgart's Wilhelma is a must for both zoo and botanic lovers. The zoo is in the Umweltzone but there're several good opportunities with the underground.
(extra) Day 5 : Nurnberg Zoo
Day 6 : Plzen
Day 7 : Prague
Day 8 : Dvur Kralové
Day 9 : Usti Nad Labem or Liberec + Dresden Zoo
Day 10 : Leipzig (Umweltzone)
(extra) day 11 : Halle Bergzoo (Umweltzone + Magdeburg Zoo.
Other option: Wuppertal Zoo + Krefeld Zoo. In fact, Wuppertal is a must: very pleasant zoo with some excellent exhibits and quid a good number of rarities.
Day 12 : Burgers' Zoo
Day 13 : Antwerp Zoo. Possibly manageable with Planckendael Zoo in summer: Antwerp has a lot of species and buildings, but is very compact. And both zoos are close together.
Antwerp Zoo is situated in a low emission zone. It will take you an hour driving from Antwerp to Mechelen/Planckendael (maybe less off rush hours). Public Transport (train and bus) probably the same (if you plan well). I can give you more information on public transport and/or parking options if needed.
Day 1 : Pairi Daiza
Day 2 : Frankfurt. Keep in mind that the zoo is situated within the Umwelt-zone with restricted access for vehicles (you'll need a permit). You can take the 661 highway, exit 8, crossing the railway heading to the Eintracht Frankfurt football stadium, park nearby and take the underground U7 at the Johanna Tesch Platz or the Gewinnerstrasse underground stations. Afterwards you have excellent acces to the A3 Nurnberg-Plzen or the A5 Heidelberg-Karlruhe-Stuttgart
(extra) Day 3 if you heading to Stuttgart: Heidelberg Zoo and Karlsruhe Zoo are easy to combine. Stay in Heidelberg and enjoy the historic old town. The zoo is outside the Umweltzone in Heidelberg, and within (but at the edge) in Karlsruhe. Both are pleasant zoos with varied collections.
Day 4 : Stuttgart's Wilhelma is a must for both zoo and botanic lovers. The zoo is in the Umweltzone but there're several good opportunities with the underground.
(extra) Day 5 : Nurnberg Zoo
Day 6 : Plzen
Day 7 : Prague
Day 8 : Dvur Kralové
Day 9 : Usti Nad Labem or Liberec + Dresden Zoo
Day 10 : Leipzig (Umweltzone)
(extra) day 11 : Halle Bergzoo (Umweltzone + Magdeburg Zoo.
Other option: Wuppertal Zoo + Krefeld Zoo. In fact, Wuppertal is a must: very pleasant zoo with some excellent exhibits and quid a good number of rarities.
Day 12 : Burgers' Zoo
Day 13 : Antwerp Zoo. Possibly manageable with Planckendael Zoo in summer: Antwerp has a lot of species and buildings, but is very compact. And both zoos are close together.
Antwerp Zoo is situated in a low emission zone. It will take you an hour driving from Antwerp to Mechelen/Planckendael (maybe less off rush hours). Public Transport (train and bus) probably the same (if you plan well). I can give you more information on public transport and/or parking options if needed.