The old describe-a-picture thing could be ho-hum if they've already done it a lot in school, but if they could bring some vacation pictures or a family album, maybe pictures of a pet, that might be something they would enjoy talking about and that would help you get to know them and find out other things to ask about. Or you could find a general-interest magazine with lots of different pictures, and see which ones they gravitate to.
Icebreakers for the younger one might be something like 20 Questions, or I Spy, or the game about 'I'm packing a suitcase and going to ...'
For pronunciation and fluency you could read children's poems or sing songs or rounds -- not pop songs, but folk songs or even nursery rhymes. Maybe not as topical as current Top 40, but on the other hand fun to see how children in different countries grow up, what songs 'everyone' is expected to know.
Jokes or riddles could be fun once or twice; you might have to explain a few puns, but then they would have something they could practice and maybe even tell in English class. Classic ones like lightbulb jokes or knock-knock jokes have a lot of variations.
You could play a board game and talk through each step in complete sentences. What are you doing? I'm rolling the dice. What did you get? I got a 7. How many squares can you move? I can move seven squares. Or especially for the older one, a trivia game, if you can find one in English, like Trivial Pursuit, or something about geography or history.
A less fun, but more useful, little exercise is just transforming sentences, which you can make into a sort of game. You just change one word each time:
I have a big box. Elephant.
I have a big elephant. (or: The elephant has a big box.) Your grandmother.
My grandmother has a big elephant. Attic.
My grandmother has a big elephant in the attic. Yesterday.
My grandmother had a big elephant in the attic yesterday.
You can adapt that kind of thing to easy changes or harder ones, depending on whether you're practicing nouns, verbs, articles, singular/plural, whatever. Not for more than a few minutes at a time, and if you're asking all the questions as the teacher it usually helps to plan them out in advance, but it forces students to think fast and use grammar.
If you meet at your or their house, a fun thing to do might be a hands-on mini-project, like cooking something really easy or doing a little craft project and talking through it step by step.
If you can go outside together, it could also be fun to play tourist, walking somewhere and giving directions or pretending to be a tour guide. Or even staying at home, one person could pretend to be the waiter at a restaurant, or the clerk in a shop ... After they get more confident, you could even go in different rooms and call each other on a cell phone -- that's a practical skill that they can really use later.