The first route I would choose
Give Old Town time, but do not let it swallow the whole city.
- Start with Old Town while the streets are still fresh.
- Add Central Market when food or weather cover helps.
- Use the river edge to reset the day.
Old Town deserves the first look: church towers, narrow lanes, courtyards, and that slightly theatrical Baltic texture. But Riga becomes more interesting when you step out of the postcard and let the market or river change the pace.
I would not try to see every landmark in one pass. A stronger day has one main walk, one practical stop, and one relaxed ending near dinner.