Paper & pen games like tic tac toe & hangman
Make up stories together; elaborate & use a lot of fun descriptive words (something isnt just big, its gigantic/huge/enormous/gargantuan...., not just pretty but gorgeous or frilly)
'What if' questions are fun at this age; what if you had a flying horse, where would you go?....What if Pocahontas came to visit you, what would she think of all the modern day ammenities? ... what if you woke up tomorrow and your hair & eyes were purple...
If you are okay with her on your computer, there are quite a few fun sites, and educational too; www.starfall.com for reading and stories, www.pbskids.org, www.nickjr.com, www.barbie.com (my 6yr old loves this one the best cause she is just sooooo into Barbie right now). But you can also google 'online educational games for kids' to find more that might suit her.
have her bring an extra outfit to get wet & muddy playing outside (if it will be warm enough to play in the rain &/or mud)
unpack a box, cut some decent size holes in it, mark each one with a number to score, then crumple up some paper to use as a ball and have a tossing game.
Play peek-a-boo with the baby. Also can do this with toys, covering them up with a blanket or washrag & having the toys hide then peek out.
depending on how your floors are; lay the baby on a blanket & have her pull him/her around the house on the blanket (this is a fun sensory game for babies)
On the same note, can the baby sit up in a box for her to push around the house?
If she knows the wheels on the bus song, she can sing it to the baby & move his/her arms & legs to the movements.
She can do the five little piggies "this little piggie went to market" with the baby
see how many different ways she can think of to get across the room; hop, jump, skip, roll, crab walk, slither...then exempt walking & running, and time which one is the fastest (a lot of cell phones these days have timers or stop watches, there is a computer program too I just don't remember it)
If you find a timer & she's allowed to run somewhere in the house, time her running in a circle, or taking a tour around the house stopping in each & every room and see how long it takes her, then have her try several times throughout the day to see if she gets faster
Do you have food coloring in the kitchen? You can have her make your meals all the wrong colors...water & milk too!
Rhyming game; one of you picks a word, then you both try to say as many words you can think of that rhyme. Your choice if you are allowed to make up works like Dr Suess books or not. (book=look, took, nook, cook...zook, puk, quook)
Add a twist; say some of your favorite nursery rhymes, but when it comes to the rhyming words, say a different word that rhymes instead, you could be rolling with laughter!
Alphabet game; pick a topic like animals, colors or food, then name one for every letter of the alphabet
Remember some tongue twisters & see if she can say them (peter piper's pickles, betty bonnet's butter, selling seashells...)
Let her put makeup on herself & you...can decide ahead of time if it should be nice, or clown-like, or nice with extra sparkles
teach her to make a paper airplane, then have flying contests
have you ever done origami? there are simple ones she should be able to do at 6 years old, I would check online
Do you have a digital camera she can use? This age usually loves to take pictures & often have a unique view of things.
I like the other ideas listed too, I tried not to repeat. As long as you keep talking with her & engage her in what you are doing, she will have fun, even if you don't get to any of these activities. If you can not yet find your crayons or colored pencils, does she have some she can bring over? Crayons and paper can go a real long way at this age. Best of luck & I hope you all have a great day!