It is useful to understand that although from 1940 to 1991 Latvia was a constituent republic of the USSR, the official language is Latvian. However, a significant minority (up to 40% nationwide and possibly just over 50% in the capital Riga) is Russian speaking. The majority of ethnic Latvians living in the city, not only those old enough to have attended school during Soviet times, can also speak and understand Russian. However, many prefer to converse in Latvian. English and also German are widely understood at places regularly visited by tourists and foreigners but you may be out of luck when leaving the city centre or visiting places off the beaten track.
A bus line from Riga, 45-50min for approx. 1,5Ls
Electric train line from Riga in 50min for approx. 1,3Ls
Jelgava is in coast of river Lielupe. River Lielupe is connect to Baltic sea.
You can rent taxi (if arrive from Riga or Riga airport).
Palace on the island of river Lielupe. Similar palace to Rundales and Winter Palace in St.Peterburg, created by Bartolomeo Rastrelli. Academia Petrina - currently museum. Several interesting churchies.
There is few clubs/pubs.
Most popular are Tonuss - club, with several halls. Place with a lot of young people. Jelgavas Četri Balti Krekli - club where play only Latvian music
It's possible to do tandem or solo skydives at Jelgava airfield. More information at Latvian FreeFly Peppers website 
"Brainstorm", probably the most popular rock-band from Eastern Europe, has emerged from a craddle called Jelgavas 1. vidusskola (Secondary School No 1), where also such National talents as A. Skrastins, A. Vaznis, E. Radzina, A. Skele, E. Repse have made their first steps in the world of fame.
Latvijas Lauksaimniecibas Universitāte - University of Agriculture of Latvia is a well recognized university.