It takes us less than 2.5 hours to drive to Fuessen by autobahn (A8 to A7). However, you could take my favorite drive in Germany along Hwy 312 which leaves the Hwy 27 freeway to Reutlingen. You'll first catch glimpses of fairytale-like Lichtenstein Castle ( www.schloss-lichtenstein.de ) from below, and after ascending the steep front of the Swabian Alb ( www.schwaebischealb.de ) the turnoff to it is at the traffic circle. When returning to this point, it's well worth going half way round the circle and taking the road toward Münsingen to Gomadingen, where you can turn off along the idyllic Grosse Lauter River to Marbach and Germany's oldest state stables ( www.gewstuet-marbach.de ) for close up views of the magnificent stallions in their stalls. Continue down the river and you will pass one of Germany's highest concentrations of castle ruins, most of which are visitable. Buttenhausen has a lovely Jewish cemetery on the hillside across the river. At Indelhausen, take the road to Hayingen and continue on to Zwiefalten. Along the way will be a cave only enterable by boat. Zwiefalten has a lovely former monastery church. Continue east on Hwy 312 and by Riedlingen (a pleasant city) you will cross the Danube. Probably at the first light to the right is a cheese factory with a sales room if that interests you. On your left is the Bussen, Upper Swabia's holy mountain, but the pilgrimage church on it isn't that good.
Biberach an der Riss ( www.biberach-riss.de ) is one of my favorite towns in Germany, nothing spectacular but just downright pleasant. I love the church there, perhaps because I was married in it, a nice blend of ornateness and simplicity. Cafe Kolesch on Gymnasiumstrasse is the best Konditorei for over 100 kms around (up to Stuttgart, Munich or Zurich), their Wielandstorte is superb. Behind it is one of Germany's oldest houses, if not the oldest as records were poor back then.
A pleasant detour is to see the "world's most beautiful village church" in nearby Steinhausen.
Continuing on from Biberach on Hwy 312 you will pass by Ummendorf, my wife's home village. The brewery restaurant has what we consider to be Germany's best Maultaschen, and the beer is excellent too, nice to wash down with their special dark Placidus Cobaldus beer. The church (not chapel) across the road is worth visiting, if for nothing else but to see how nice a typical Upper Swabian church can be, and museums would kill for one of its carved figures. The storks may be in residence in their nest on the palace across the road.
Continuing on, Ochsenhausen has a large visitable monastery. Very impressive when viewed leaving town as it sits well exposed on the hillside. Instead of getting on the A7 in Memmingen, continue to Ottobeuren ( www.ottobeuren.de ) for the most impressive inside of a church you will see in Germany at the monastery, just crammed full of more beautiful Baroque religious items than can be easily comprehended. Then get on the A7 to Fuessen.
This route has the advantage of being a very direct route, an excellent very pleasant drive, with a very good assortment of places along the way to visit. You also won't get caught in autobahn traffic jams.
If you go via Lake Constance, the drive will be much longer, but I would recommend taking the road along the Danube River between Tuttlingen and Sigmaringen (excellent castle/palace- www.hohenzollern.com ). It is simply idyllic with castles and palaces perched atop the cliffs ( www.donaubergland.de only in German). From Sigmaringen, head to Pfullendorf, Heiligenberg, Salem an Uhldingen-Mühlhofen on Lake Constance, and a short distance away will be Meersburg ( www.meersburg.de ), the loveliest town on the lake. Leaving the lake, Wangen is a lovely town to visit. I would only recommend driving this way if you have several days to do the trip, and that won't even be enough, as it's a shame to drive by so many interesting places without stopping.