I am Liverpudlian but rarely go into town but here are some restaurants near Arena I have been to. Maray Albert Dock Middle Eastern Yotam Ottolenghi style food and delicious. What’s Cooking Tex Mex meaty menu The Smugglers Cove traditional English fish chips pies etc and flavours from abroad. George’s Great British Kitchen further away in Paradise street is nice posh fish chips salads etc reasonably priced. Bon Pan Clayton square buffet restaurant world food choice is endless. Casa Italia Stanley street nice food best to book gets busy. We met our daughter at the museum of Liverpool life recently ate there for lunch was ok but wasn’t that impressed. I hope your enjoy your day out.