We stayed a few nights in ABQ so we just waited until the next day to pick up a car. In our case, we found Hertz to be cheaper so we took the Railrunner up to the Montano Station and Hertz picked us up from there.
If you are visiting ABQ for a day or more first, then skip the car until you need it. The nearby Hotel Andaluz is very nice and is an easy two block walk even for us seniors. The Parq Central is a little further but they have complementary pickup and drop-off at the train station. Both hotels have a quick, close, inexpensive and short ride to Old Town where you can enjoy your first full day. Or stat at an OLD Town hotel or B&B. Bus from Amtrak Station or short taxi/Uber ride down Central Ave. Moreover, if you are arriving on a Friday or Saturday, you can have a pizza dinner (very good & that's from a NY Italian) at J C's New York Pizza Department in downtown near the station on Central. Sit outside and watch the awesome parade of weird cars and pickups cruising by. Loved it!
Remember, the RailRunner train will take you from Abq to Downtown Santa Fe and you can walk or take the free shuttle from there to Santa Fe Old Town (where car parking can be iffy).
THEN after seeing Old Town and Santa Fe, you get a rental car.
Note that RailRunner train (listen for the cartoon beep-beep as the doors close) and Albuquerque bus system offer discounts to seniors. Veterans with VA card ride RailRunner (and I think city buses) for free.
We lived in NM for 22 years, five in ABQ and my brothers & sister, their kids and grandkids live there so we now go back by train. We have stayed at both the above-named hotels and did exactly what we suggested above.