These neighboring properties (Courtyard and Residence Inn) are 4 blocks away from downtown's main drag but still within walking distance of Indy's restaurants and shopping. The Courtyard at the Capitol runs about $20/night less than the Residence Inn (and, $20-$50/night less than Courtyard Downtown), but if you have a family to feed, the latter's free breakfast each morning will quickly make up the Andrew Jackson.
Both offer complimentary parking and typical accommodations for their respective brands. Courtyard's workout option is slightly more elaborate than Residence Inn's. Both provide equipment in tiny rooms, but Courtyard's bikes and treads (Precor) appear newer and more friendly (foot straps provided).
Since the hotels are both Marriott-owned, staying at one and exercising at the other is an option, but athletic-minded travelers will surely prefer the 7 to 10 minute walk to the off-site fitness venues: NIFS for a health club, the Natatorium for a lap swim, and/or the White River for an outdoor jog.