Is it worth staying in the old/historical district, or are there other locations that are recommended?
The "old" district isn't particularly old; its most famous non-religious structure (a guild hall) was rebuilt in the 1990s.
It's not a particularly spread out city, attractions-wise. If you're a walker, you'll get your exercise, but it's all doable. And if you like unusual architecture, that national library is trippy.
I'm visiting Riga in a few weeks. Does anyone have any restaurant/bar recommendations? I'd like to try somewhere not far from the old town but more local diner orientated.