Depends on where you are travelling from and what time of year you want to go.
If you are in Europe the best place and cheapest out of season is canary islands as they are tax free and have a great year round climate.
La Palma is one of the smallest of the islands, but is like a Hawaiian island very green and lush and unspoil. Many people consider it one of the most beautiful islands in the world, certainly in Europe. Don't confuse la Palma with las Palmas which is capital of gran canaria!
Fuerteventura has the best beaches in europe and is a lot quieter than its bigger neighbors of Tenerife, gran canaria and Lanzarote.
Galapagos islands are wonderful, as is mainland Ecuador.
Anywhere around the amazon is beautiful.
Sri lanka is great, Maldives as well.
I've been to all these places and I work in travel industry, so if you want to write to me, or edit your question, but some more details I need....,Where you want to travel from, what do you like, quiet, night life, sightseeing, islands, mountains?? Let me know and I will write again tomorrow gotta go now, flying to Prague!!
Just looked at your profile so know you are in Germany and are having a baby.
So long distance travel is out as is anywhere too tropical!
So canaries is good October to may is ideal with small baby.
Or for a wonderful and cheap holiday try croatia easy to get to from you, very cheap, beautiful beaches, lots of history. Island of krk very nice.
If you like volcanoes then canary islands is definitely the best place for you to travel in Europe. Tenerife has as its center piece mount Teide which is the biggest mountain in the whole of Spain and probably the biggest volcano you can safely visit in the whole world! You can take a trip almost to the top, from where you get great views of the island and on a clear day you can see all the canary islands!
The south of the island is dry and very sunny and has all the night life, the north is very green, the national park is called las Canadas, because it looks like a small Canadian forest! Great mixture of everything for you here!
Stay in playa de las America for the best night life. But do some trips or hire a car to get the best from your holiday.
Icod de los Teide is one of the oldest trees in the world. Much history to be seen, Christopher Columbus landed in Tenerife on his way to America.
For shopping go to the capital Santa Cruz, tax and duty free, so many great bargains particularly on perfumes, sunglasses and electrical goods-half the price of most of the rest of Europe!
Take a day trip to the nearest other canary island-la gomera, only 30mins by boat. beautiful island, locals even have their own unique whistling language, to communicate across the many valleys. also try a day trip to la Palma, you'll love it!
This is your best choice in Europe. Other than that all the other places other people have mentioned are great, I've been lucky enough to have been to most. But to fit your criteria, and my personal favorite you can't beat Bali in Indonesia, best place I've ever been-been 3 times now and will go again. not sure how cheap it,ll be from states though. Good luck with the new baby, have a great life.