Riomaggiore is the first Cinque Terre village when arriving from La Spezia direction and the start of the scenic walkway above the sea called Via dell'Amore, connecting it with Manarola, the next Cinque Terre village. For a nice lunch in Riomaggiore, Serena of Wishversilia recommends Dau Cila Restaurant, overlooking Riomaggiore's harbor, for excellent fresh seafood. Serena is a travel guide for this area so knows the restaurants well. For more about a place to taste wine, where eat in Vernazza, and an update on the current situation in Monterosso, see her post Back to Five Lands.
If you're planning to hike in Cinque Terre, even just on the Via dell'Amore, you'll need to buy a Cinque Terre Card. Find out more about the trails with this Hiking Trails Map.