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 (Koblenz) guards with them. Sometimes work in tandem with waiting municipal police - be aware! They're money-grubbing gangs working in symbiosis.
Sixxt bicycles can be rented for quite cheap, and Panda taxi is the cheapest taxi if you need it.
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, and so on. It is called Lattelecom-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 and in Old Riga, as well as Vērmanes dārzs(park). Police generally aren't annoying and don't run buskers off, so they shouldn't be a problem.
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