We did the bike tour from this company, and they were great (they don't cover old town OR the central market on the bike tour, so definitely don't miss those in your spare time):
https://www.rigafreetours.com/
It is a really sad arrival spot in the middle of a cargo shipping field without any cruise ship facilities...but they had 10 buses ready for us when we disembarked and tourism staff from the city were there to answer questions. Took about 20 minutes to arrive, but due to traffic took about 35 to return. Last shuttle to the ship was 6PM, and we caught the 5:30PM and it was PACKED with people standing / sitting on the floor. They drop you on the main road by the river, right next to a public toilet (link below), a few blocks from the old town and tourism staff meet the buses there too and provide maps and mark locations for you, HOHO buses are there as well.
https://goo.gl/maps/DAeaqysnk69oURX6A
**Should share an important piece of info which is that since this "port" is inside an active shipping port facility, taxis are NOT allowed to enter (and some refuse to go this far away to the middle of nowhere where they won't get a return fare). Some ship staff tried catching taxis to get back on time and had to be dropped off at the facility entrance, far from the ship and catch the bus from there**
Overall, Riga is a glorious beautiful city and it is a shame the first impression is so bad, but they are doing the best they can with their port situation and larger ships.
In addition to the sites seen on the bike tour (including art noveau district), our favorite spots were the old town, the central market (incredibly large and diverse but more for getting a "taste" of local shopping goods, not tourist crap), and the Library (easy walk across the river, a cool modern building with a few free exhibits inside).