Parafoil kites, and their cousins the sled kites, are the most convenient kites to pack and take anywhere. The foils are completely soft (no sticks) and will fit in a corner of a travel bag, or even in a pocket. They can be out of the bag and into the air in no time, and are very reliable fliers.
Sleds usually have very thin spars to give them form, but can be folded. Most of them use the drogue tail supplied with them as the bag when you have finished flying - very convenient! Bigger models can have a lot of pull and may be used to lift "line laundry," which is the term for items hung from the kite line to enhance the display.
Sizes vary from those suitable for young children up to ones that can give an adult a stiff workout in a strong wind. For the biggest, the Megasled 81, you need to have somewhere to tie down the kite, as hand-flying for long or in high wind would become difficult.
Be sure to follow the recommendation when ordering the line for your kite if none is provided with the one you choose. Proper line of the correct test strengh is essential to avoid problems.