We did a week in Croatia last summer and had a great time. We stayed at the Lafodia Resort on Lopud island, off the coast of Dubrovnik. There are lots of islands with hotels and resorts. We did a little bit of introductory sea kayaking (which we both enjoyed a lot) and some snorkeling, and did a day trip to Dubrovnik which was tons of fun.
What exactly do you want to do in Croatia? Are you looking for something relaxing? Something outdoorsy? Something educational/historical? Something kid friendly? I've been to Zagreb, Samobor, Plitvice Lakes, Krk, Pula, Rovinj and Roc. I was there at the end of October and while the weather was mild it was not exactly warm or beach weather.
Wanderista can probably help you out with a bit more information
Beach for sure! Just me and my son to plop and play in the sand, with the option of some night outings as a family. Was wondering about the weather, maybe I'll move it up to be our Aug trip as opposed to Oct.
Croatia does not have a lot of sandy beaches so that will limit your destinations. Most of the beaches are made up of small rocks and pebbles or there is no beach- just a staircase into the water.
I know that there is a decent sized mud flat on the island of Krk that my nieces love to visit in the summer but I cant remember what side of the island it is on; all I know is that its down the road from grandmas house.
September would probably still have nice weather along the coast and its usually the tale end of tourist season so the beaches wont be as crowded and things will be a bit cheaper.
If you like cheese make sure that you have some Paski Sir; its cheese from the island of Pag.
October in Croatia is going to be cool. It is not really beach weather anymore by then if you really want to swim. Indeed, most of the hotels along the coast close in November and their staffs leave. You'd be there at the end of the season then. October is a good time to go to Istra/Istria which is the peninsula near Slovenia and Italy. It is a good time for agritourism especially because it is truffle season. There are places like Motovun where that is the high season because of this. Basically, if you wanted to go to Istria and have a vacation in the countryside, it would be a good time of year. Along the coast, the prices will be lower and the weather will be cooler. Cold temps set in quicker there than in the States. Even by September, it can be chilly in some parts of Croatia and cool breezes can start to blow.
August is a good time to go for the weather, it is also the high season in Croatia. That's when most Europeans take their vacations and Croatia is very, very popular with Austrian, German and other assorted tourists who arrive en masse for up to a month at a time. That is fine because everything is in full swing then and it's a great time to do the beaches but just be prepared for that. You will probably want to book accommodation soon if you want to go then because it fills up. If you are flexible about your dates in August and you are able to book accommodation relatively soon, then that is when I would go for the kind of vacation that you want.
There are some sandy beaches in Croatia but a lot of people don't know about them and they are often fairly secluded. I've been to #1 on Alleinsein's list which is one of my favorite beaches ever. Actually the thumbnail in my profile is from near there. It is located somewhat north in the country so the water is a bit cooler and it is also fairly remote. It is any area with sleepy villages and less infrastructure than other parts of the country. I have been to some others that aren't on the list and I'm familiar with nearly all of the places in that list though I did not go to some of those beaches. I have been to some of those cities like Trogir, Šibenik, Dubrovnik and Zadar but I tended to focus more on touring the cities there and also I went to a lot of pebble beaches. It's a good idea to bring good thick flip flops in case you want to do that. You can leave them along the shoreline while swimming, lots of people do that. I also boated along the coast around places like Korčula and Hvar. I also went to Montenegro which has some sandy beaches too, I went to Budva there. It is possible to daytrip into Montenegro from Dubrovnik if you prefer staying in Croatia.
Going to Lapad near Dubrovnik would probably be the most straightforward option but it is also possible to boat around Dalmatia and stay on a few different islands if you want to see more of the country. If you have an interest in that, I would look at the Jadrolinija website Jadrolinija - Croatian national ferry service. That is the main ferry service. As far as booking hotels goes, there are several different ways to do it. I know that we used booking.com to arrange some of our accommodation especially in Dubrovnik. You can use any website, I just know that one lists a lot of the hotels in that part of the world. Some of the islands had Croatian websites which I think we also used. It is also possible to rent private accommodation through a service. We rented an apartment in Bol that way. I think it was a listing service for vacation rental apartments. I liked it. We were able to stay in a flat with a kitchen, private bath and terrace with sea views that way. I would guess that some of the other places in Dalmatia have that as well.
Let me know if you have any specific questions and you can always PM me if you want. (The places that I mention visiting in this post are just the ones near the beaches listed in Alleinsein's article. I have experience with some other parts of Croatia as well.)
If you click that and then there are several other entries as well, my friends went last spring and took their kids, including a 5 year old, hope it helps!