Riga is small enough that it can be covered easily on foot - the major attractions and locations anyway. Public transport is very expensive due to the company that runs it being a corrupt black hole for finance. If you are a traveler you might get away with blackriding if caught, but the controllers are often rude and aggressive and have private security guards with them. Sometimes work in tandem with waiting municipal police - be aware! They're money-grubbing gangs working in symbiosis.
You cant blacride trains, control will check for tickets on each station
Sixxt bicycles can be rented for quite cheap, and Panda taxi is the cheapest taxi if you need it.
Accommodation & Wild Camping
Zakusala island wild camping by walking - from centre the island on Daugava river where TV tower is located in the middle of Salu tilts bridge. It's within walkable distance from the city center and really quiet place with nothing else really there. Both tips of island are covered with bushes and trees so it is easy to find a place to hide away. You can swim on the start of Salu tilts bridge (city centre side of it)
Mezaparks wild camping by tram - next to Riga Main Railway Station get in tram nr 11 direction to Mezaparks, get out at last stop Mezaparks. There is forest park with big lake where you can swim. Police is cheking main park roads next to Zoo for safety so camp in distance from there. For camping best place will be around Sarkandaugavas Kapi bus stop thats 1.5 km walk away on Meza prospekts direction to Sarkandaugava.
Shower & swiming
You can swim on the start of Salu tilts bridge in Daugava river (city centre side of it) or catch a tram 11 to Mezaparks / Zoo and swim in Kīsezers lake
Best spot for cheap but intresting and good quality food is Riga Central Market
In the very center it is almost everywhere - the city provides free public wifi that you can catch in some parks, some larger streets, near the central station, supermarkets, fuel stations and so on. It is called TET Free, but if you can't find it, there will definitely be another free wifi connection somewhere nearby.
Local buskers perform in the tunnels near the central station/cinema/Old Riga, Laimas pulkstenis, Vērmanes dārzs(park). Police generally aren't annoying and don't run buskers off, so they shouldn't be a problem.
Kaņepes kultūras centrs - culture place with cheap drinks and music events
Reigys Ausmeņa Kebabs - best kebab in town
Tallinas kvartals - art district
Lastadija - art district /take a look at Latvijas Zinatņu Akademija science academia building/
Pier at Daugava river @ Andrejostas iela - cool place to chill and drink a beer /no shops there visit Spirits&Wine before/
Latgalite - bigest flea market