Bit late to the question but it is my old hood.
Pub - The Harrison, The Queens Head
Pub & Food - The Easton - great food!
Cocktails - Exmouth Arms basement bar.
Cocktails - Bourne and Hollingsworth
Fish and Chips - Kerbisher and Malt
Chips - Calthorp Arms - I rate their giant plate of chips!
Restaurants - Moro, Quality Chop House, Caravan (breakfasts!) Lots on Exmouth Market to explore.
Bakery -Aux Pains de Papys - proper french bakery
Bar - 06 St Chads Place
As mentioned Paolina Thai - cute authentic, but not mind blowing...