Up a hill at the back of Argassi you will find Target Restaurant, this is a lovely restaurant with a great greek night and excellent service with friendly staff with the most beautiful view over Argassi and Zakynthos town.
On to Zakynthos town and you have the main port road (pic 1) with plenty of cafe's and restaurants my favourite along the port road is The Village Inn. Then at the end of the port road you have Solomos Square (pic 2) where you can sit outside a cafe and watch the world go by, Base is a great place to relax with a ice cold coffee (frappe), then maybe if you wanted to eat away from the traffic of the port road try St. Markou Square (pic 3) with 4 restaurants to choose from all good.
And my first tour of the island for you wouldn't be complete without a trip to Bocali up above and behind Zakynthos town, this is a must even if its a taxi journey for the day or night, i'll let the pictures speak for themselves.
Well thats my first guide done and will post more as i do my seasonal tour of the island. Hope your as lucky as me and get to visit some of the places i've shown.