There are quite a few destinations in Greece available 16th to 18th June for around 390 euro return (I checked CHQ, HER, RHO) if you fancy that, or they are all about 10 euro less the following weekend. From 16th to 18th you could go to SKG for 335 Euro return. It's a nice city for a weekend break although you'd get there late Friday and leave quite early Sunday.
It won't take you too long to search for more options. To be honest, you've left it quite late and have pretty restrictive dates so I think you're being unreasonable if you expect to get something for any less than that, in the tourist season and only at weekend (and have somebody else find it for you too!). Those took me around three minutes to find using just the A3 site.