Mexico City: museums, markets and the Centro on foot
Start with the Centro Histórico, where the Zócalo, the Palacio Nacional murals by Diego Rivera and the Templo Mayor exterior viewing platform cost nothing to visit; the Palacio Nacional is free with photo ID, and the Templo Mayor site itself has a small paid ticket but the surrounding plaza and the Metropolitan Cathedral are open to all. The Museo Nacional de Arte on Calle Tacuba and the Franz Mayer Museum run free-admission days, typically Sundays, though schedules shift, so confirm at the door rather than relying on a guidebook. Walk south to the Mercado de San Juan and east along Calle Regina in the Centro for a feel of the neighbourhood without spending a peso.
The bigger free win is Chapultepec. The park itself, the lakeside promenade and the views from the Castillo approach are free; the Castillo and the Museo Nacional de Antropología charge admission but both run free Sundays for Mexican residents and often for visitors with valid ID, though this is inconsistent. The Museo Tamayo and the Museo de Arte Moderno sit in the same park and are small enough to combine in an afternoon. For neighbourhood wandering, Roma Norte and Condesa are walkable and green; Coyoacán's Jardín Centenario and the Frida Kahlo house exterior are worth the Metro ride to Viveros/Coyoacán station. Allow a full day for Chapultepec alone.
Guadalajara: free plazas, murals and the Tapatío rhythm
Guadalajara's Centro is refreshingly walkable and free to roam. The Plaza de Armas, the Palacio de Gobierno with its Orozco murals (free entry, ID required, closed Mondays) and the Hospicio Cabañas courtyard are all no-cost or near-free; the Cabañas chapel murals carry a modest ticket, but the courtyard and surrounding plazas do not. The Mercado San Juan de Dios, the largest indoor market in Latin America, is free to enter and best visited in the morning when the produce and leather stalls are busy. The Templo Expiatorio, a neo-Gothic church on Avenida Hidalgo, is free and worth 30 minutes, especially in the late afternoon light.
For green space, Parque Agua Azul near the San Juan de Dios market offers free paths and a small aviary, and the Bosque de Colomos in the northwest near the Zapopan border is a cool, shaded escape with free entry. The Paseo Chapultepec and Avenida Vallarta are good for an evening stroll; the neighbourhoods of Americana and Providencia are leafy and safe for walking. On Sundays, the Via RecreActiva closes major roads to cars from roughly 8am to 2pm, which turns the city into a free cycling and walking circuit. Bring your own water; vendors charge for everything, and cash is still king in the markets.
Getting between them and where to base yourself
The Guadalajara–Mexico City corridor is well served: intercity buses from the Terminal Central de Autobuses del Norte in Mexico City to Guadalajara's Central Camionera take about six to seven hours and are comfortable and frequent, while flights from Benito Juárez (MEX) to Guadalajara (GDL) take about 1 hour 15 minutes. If you are booking a hotel, base in Roma Norte or Condesa in Mexico City for walkability to Chapultepec and the Centro, and in Americana or Centro in Guadalajara for easy access to the plazas and the Via RecreActiva. Both cities are best visited in the dry months, roughly November to April, before the rains set in from June.
For a two-city trip, the sensible split is four nights in Mexico City and three in Guadalajara, not the reverse — Mexico City's free sights are spread wider and reward a longer stay. Budget hotels in Roma Norte and Condesa typically run mid-range, while Guadalajara's Centro and Americana offer similar bands with more space for the money. Skip the tourist-train loops in both cities: they charge for what you can walk in an hour. Do check museum free-day schedules the week you travel, since they shift around holidays, and carry photo ID — several free-entry government buildings require it at the door.
What I would book and what to skip
I would book a small hotel in Roma Norte within walking distance of the Museo Nacional de Antropología and the Metro at Insurgentes, then take the bus to Guadalajara and stay near Avenida Chapultepec for the Via RecreActiva and the Centro. That pairing keeps your paid transport low and puts the free sights on your doorstep. Skip the paid observation decks in both cities; the free views from Chapultepec's upper paths and from Guadalajara's Plaza de Armas are enough for most travellers, and the money is better spent on a good meal in the markets.
Do not over-schedule. Both cities are best on foot, and the free experiences — murals, plazas, markets, parks — are the ones you will remember. Carry cash for market food and small tips, keep an eye on your belongings in crowded markets, and confirm opening hours the day before you go, as public buildings in Mexico frequently change schedules. If you are travelling in the rainy months, plan indoor free stops like the Palacio de Gobierno in Guadalajara and the Palacio Nacional in Mexico City as backups. Book your hotel early in the dry season, when demand in both cities peaks.