Will you be arriving in your own car or on public transport? I'd say that once you're finished at Migración take a taxi or drive to Bella Vista Mall (pronounced MOLL) on Avenida Sarasota.
There's a supermarket, a ferreteria, home decor, boutiques, and all sorts of shops, and on the 2nd level they have a good choice of eating places. Nothing too fancy - pizza, burger, mexican, crepes, pseudo-Starbucks place, etc.
The advantage is that you can get everything under one roof without having to traipse around the capital, which is complicated if you're not familiar with the place.
If you want more charm and character, head for Calle El Conde in the Colonial Zone. There are plenty of eating places in the area as well as shops, but less glitz.
If you need any help with specifics, ask here or send a PM.