He went to work in St Petersberg, which is just up the coast. No idea if he sailed or drove, but it seems quite likely to have been on his way regardless of where in Europe he was before (Switzerland?).

(TLDR: likely on his way, but did he stop there?)

Yes, he was in Switzerland, in Basel. Googled a bit. http://www-groups.dcs.st-and.ac.uk/history/Biographies/Euler...:

"Euler left Basel on 5 April 1727. He travelled down the Rhine by boat, crossed the German states by post wagon, then by boat from Lübeck arriving in St Petersburg on 17 May 1727."

Still inconclusive, but given that we know this, I would say chances are non-zero that the sources this was derived from spell out where that ship made stops.

One could also look at his journeys from Leningrad to Berlin and, years later, back, but both were after his publication on the 7 bridges problem.

*rode. I dont think one drives a wagon. Euler was born in 1783.

Someone probably drove the vehicle in question for Euler but:

b.2.b One who drives a vehicle or the animal that draws it; a charioteer, coachman, cabman, etc.; also, one who drives a locomotive engine. (Often with defining word prefixed, as cab-driver, engine-driver, etc., for which see the first element.) [...]

c 1450 St. Cuthbert (Surtees) 6016 All þe dryuers ware agaste þat þe sledd suld ga our faste. 1581 Savile Tacitus 93 (R.) Buffons, stage-players, and charet drivers. 1725 Pope Odyss. xiii. 99 Fiery coursers in the rapid race Urg'd by fierce drivers thro' the dusty space. [...]