what price range should we expect?

Budget can mean a group participation camping safari where you travel on a large truck or it can mean staying in larger lodges rathern than smaller tented camps.

To throw the question back to you, what is your land budget?

If you have 7, you are in a good position to design your own trip and make it affordable, hopefully matching your budget.

What helps is you are traveling to Kenya when it is not high season.

I agree with atravelynn that with 7 of you, you could easily design a private safari. You'll most likely need 2 vehicles and want to bring along a cook in addition to your driver/guide. There are both public and private campsites (where it's just your group). At the latter, you may be required to take an armed guard (generally from the park service of whichever park you're visiting). There are also self catering houses/bandas depending on where you go which may work for your group such as Naishi House in Nakuru http://www.kws.org/tourism/accommodation/naishi_guesthouse.html or Fishing Lodge in the Aberdares http://www.kws.org/tourism/accommodation/aberdare_FishingLodge.html

If you have 6 days/5 nights, I might do -
Day 1 - Nairobi to Aberdare NP (3 hours), it's a little too cold to camp here so I'd stay at one of the KWS accommodations
Day 2 - Aberdare NP to Nakuru NP, I would drive through the moorlands and exit out of Mutubio gate on the west side of Aberdare NP stopping at the waterfalls along the way, this will take longer but be more scenic than the highway route
Day 3 - Nakuru NP to Mara NR (6 hours)
Day 4 - Mara
Day 5 - Mara
Day 6 - Mara back to Nairobi (6 hours)

If you have an extra day, I might add it to Nakuru as you'll be arriving fairly late in the afternoon if you take the scenic route. When we did this, we entered Nakuru around 4:00pm and went straight into a game drive. It's a bit of moving around but will give you a nice variety in a short amount of time. Aberdare is a high elevation forest park that's completely different than elsewhere in Kenya. Some species you'd be more likely to see here vs other locations are forest hogs, bushbuck, reedbuck, Sykes monkeys and even with more commonly seen species such as elephants and buffalo you'd be seeing them in a different environment. There are also bongo present in the park though we've never seen them. Adding Nakuru gives you a Rift Valley lake where flamingo are present and there are both white and black rhino and Rothschild giraffe.

Another place that you could stay which is near the Aberdares but outside of the park is http://www.africanfootprints.de/en/welcome-to-sandai/ They have 2 two bedroom self catering cottages. From here, it's also a short drive to Solio which is a private reserve that I believe has the highest concentration of rhinos in Kenya (though you're very likely to see them in Nakuru as well).

Another alternate location would be the southern end of Laikipia (this would be in lieu of the Aberdares unless you had more time). There are many private conservancies in this region and you could reach the southern end such as Ol Pejeta in 3 hours from Nairobi http://www.olpejetaconservancy.org/ You can camp here or there's also the self catering Pelican House though it might not be large enough for your group and is pricier than the other accommodations I mentioned. You will start to see some of the "northern" species here such as reticulated giraffe and Grevy's zebra.

I'll top an old trip report and add a new photo link at the bottom for you which includes Laikipia, Aberdares, Nakuru and the Mara so you can get an idea of the differences http://www.fodors.com/community/africa-the-middle-east/patty-marks-kenya-tanzania-trip.cfm

At Nakuru it's likely only white rhino.
At Lewa and Solio will be both white and black. Rhino also at Ol Pejeta, but not sure whether it was white or black or both. Small rhino sanctuary at Meru and even smaller one at the very north of the Mara Reserve (believe momma/poppa and baby, which isn't so much baby these days).

I believe both species are present at Nakuru, Ol Pejeta and Meru though white are likely easier to see even on Solio. The rhinos at the Ol Chorro sanctuary north of the Mara are white, fairly habituated and closely guarded all of the time. You can approach these fairly close on foot. You may see wild black rhino in the Mara and Aberdares as well.

i would advice you to do 2 nights masai mara one night lake nakuru and two nights in Amboseli and since you are group of 6pax that's a very good number to get a discount.send me your email address and i will send you a detailed program and a discounted price
Regards