Spain, Portugal, or somewhere else?

DH has received a surprise bonus so we have decided have a bit of a break.
Trouble is we don't know where to go.  We will be taking our girls with us (ages 5 and 8 ) and the 5 year old really enjoys the beach.  Even though the 8 year old does not like sand we are leaning towards a coastal location.
The plan is to go mid/late April for 3-4 days.  We are not the party type at all and perfer someplace quiet. In the past our holidays have consisted of walking around the local area, check out historical sites, and just relaxing in our accommodation.  For example, we have really enjoyed our trips to Oban. 
 The all inclusive resorts scare me a bit-Benidorm doesn't appeal.  DH has mentioned Alicante, as he has been there on business-but is it more British than Spanish?
We usually go for self catering, but since this is a short break a hotel would be alright.
Does anyone have any suggestions?  Or can someone suggest a good travel agent? 
We could fly out of Southampton, Bournemouth, Gatwick, or Heathrow.
Thank you 

What about Greece - very child friendly. 

The Vendee in France has fabulous beaches and plenty to do.  Very French too.

What's your budget?  If you wanted to splurge you could go to Club Med on the Algarve but probably looking at a fair bit over £1,000 but you'd get all inclusive food and drink.  It'd be bound to have a very French and Portuguese feel to it.  We're considering a trip there next year.
Haven't done coastal Spain or Portugal yet but I've heard nice things.

The Vendee in France has fabulous beaches and plenty to do.  Very French too.

We were considering a Eurocamp holiday in Vendee or Brittany.  Glad to hear the beaches are so nice!  When you say plenty to do do you mean there's towns nearby to do stuff or there's lot of beach activities or sites?

The beaches are vast, sandy expanses - largely untouched.  Some seaside town are more touristy and developed than others.  If you like more activities then somewhere like Les Sables d'Olonne might suit you or if you like surfing try la Tranche sur Mer http://www.ot-latranchesurmer.fr/gb/

It's a large area - we stayed about 40 minutes from La Rochelle (lots to do there).  We explored the Poitevin Marshes (described as a 'green venice') by boat.

The best day out we had though was at Puy du Fou.  The whole family went (from my parents in their early 70s to my youngest aged 6) and we all thought it was one of the best days out we had ever had.  Hard to described - a historical theme park but with fabulous shows.  My son loved the Viking Invasion and the Knights Jousting.  I like the Roman Chariot Racing and my mother loved the incredible Bird Show.  I can't think of a bad thing to say about it!

We intend to go back and perhaps stay further north in the area - perhaps near the Ile de Noirmoutier.

We just spent a week in the quiet algarve in Portuga (just my husband and I). Usually the place is brimming with tourists but because it was the off season it was very quiet. We stayed in resort with accommadation of a small studio so we had a kitchen, living, and bedroom area. The beaches stretched for miles and the water was beautiful. It was too cold to swim though. We hired a car and was able to explore the area.. churches, museums, local pottery.  It was pretty but a week was too long for us.

I'd check on Greece, there are some nice kid-friendly places there from what I have read, and reasonably priced, as well. Just read up on it to make sure you aren't picking a "party spot" and you should find some nice places.

Thank you all so much for the recommendations!  They all sound wonderful. 
We just need to get away for a few days as we have not have the best past few months. 

Why not try Puerto de La Cruz on Tenerife, weather should be good, 4hr flight

http://www.tripadvisor.co.uk/SmartDeals-g187481-Puerto_de_la_Cruz_Tenerife_Canary_Islands-Hotel-Deals.html

Worth adding that there are two tenerifes - avoid the south of the island which can be full of boozy brits, the north (purerto) is more relaxed and upmarket and also far more lush in terms of its micro climate

Yes, exactly what english.bloke said!! I second the Tenerife suggestion... now excuse me while I day dream about taking my own holiday there

I was talking to a friend yesterday and they suggested Tennrife as well.  Thank you for the info on what areas to avoid. 
I'm getting cold feet now as far as booking someplace.  Part of me wants to put the money away-given how the economy is.  However, for once in my life I would like to throw caution to the wind and go for it!

What about Gran Canaries it's pretty cheap in April. I was looking at a week in June and it was under $1000 for flights and hotel for 4 of us. It's warm and has lots of beaches.