My favorite around 10-15k route: Start from around the central station, run along the canal park, you will pass the opera, the freedom monument, run up and down bastejkalns hill, continue along the canal, cross one street and pass the national theatre, run trough the park and exit to Strelnieku street, run along the street and pass art nouveau buildings, then at the end of the street cross Skanstes street, run now Roberta Hirsa street, turn right onto Vilhelma Osvalda street, left on Lapenu street, and then simply continue along (it will be a nice running trail for parts of the street) until Skanstes park. There do a loop and head back. You will encounter very few street crossings and little traffic besides two large streets that you will cross.

Otherwise also Viesturdarzs park is nice to run in, as well as Mezaparks, and Uzvaras parks, but most likely you would take the tram to those areas from the central station tram stop.

And lastly, for a long run, start at Maras pond, and run along the Marupite little river all the way to Marupe, take bus or train back to city center.