Hello Mara..we have spoken several times on TER LA chat about your upcoming trip through AZ. This is the official website for the caverns. The website is quite informative and includes a very good map.
Your friendly local Arizona tour guide.  

Mara - check out http://www.pr.state.az.us/parkhtml/kartchner.html

It seems the park does have a limited number of "same-day" tickets available on a first-come first-serve basis.  You might also check out the hotel where you will be staying in the area (assuming you are staying in a hotel!)  The concierge often has tickets for these events even when sold out to the public.  Arizona Inn advertises ticket availability for Kartchner Caverns tours:

http://www.arizonainn.com/attractions.htm

From their web site
Address
P.O. Box 1849
Benson, Arizona 85602
Information (520) 586-4100
Reservations (520) 586-CAVE (2283)    
Directions
The park is located nine miles south
of I-10, off State Hwy 90, exit 302.
Park Hours
The park is open 7 days a week.
7:30 a.m. to 6:00 p.m.

Cave tours: 8:40 a.m. to 4:40 p.m.

Closed Christmas Day.

Fees
Entrance per car $10.00
(4 people per car/$1.00 each additional) -
Price includes entrance into Discovery Center, park grounds, hiking areas, picnic areas, and amphitheater
$22 / night camping fee
(includes hook-ups)

Gift certificates available for purchase

Cave Tours
Under 6 years of age - free (ticket required)
7-13 years of age- $6.00*
14 years and older - $14.00*

*includes reservation charge of $2.00

Please note, we do not accept on-line reservations. You must call the reservation number to secure a reservation.Walk-up tickets remain available each day on a first-come, first-serve basis when the park opens.

Bisbee Arizona is only about 25 minutes from mTombstone/SV. Beautiful old mining town. They have a great underground tour , The Queen Mine tour, that bring you underground via a mining train. Kids seem to like it!. Plenty of neat boutiques and antique shops as well as some good restaurants for the adults.

Nogales is about an hour away from Sierra Vista. If you go, be sure to go to La Roca. A great restaurant abot 100 yards from the border. If you go at night, be sure to check out the Gentlemens clubs, (LOL) about 4-5 of them are clustered across the border entrance. They are nice, and well appointed and are nothing like you'll ever see in the US.

Of cource Tucson is only an hour away. If your staying in Benson, they do have
roping/bull riding most Sunday afternoons at the Arena Bar.

Bottlcaps