Psalidi itself is just a collection of modern hotels there is no 'resort centre' or village. The beach is a grotty black grit affair nothing nearby is much better either.
Stayed in Psalidi in September in the Iberostar Panorama. The hotel was brilliant but there is nothing really around it. It's a taxi ride ( approx 6 euros each way) from Kos town. I personally wouldn't go back to Psalidi although Kos was good.
We stayed at the Iberostar Panorama last year and it was lovely, but extremely quiet out of season. I would recommend it though. Psalidi was Ok, a small area on the outskirts of the main town - which was much more fun. Its fairly child-friendly too.
Another vote for the Iberstar Panorama !!! We went last Oct with 2 kids (3&7) - excellent ! excellent food, good pools, excellent Playbarn. Kos Town nearby with plently of island trips on offer. Good deal with Medhotels.com (kids stayed free), booked flights separately and hired a car - whole deal about £1000 - would definitely recommend going once but limited appeal to go back.