Creating budget-friendly itineraries for exploring Italy's enchanting cities and attractions can be both an exhilarating challenge and a pathway to unforgettable experiences. To begin this venture, one must prioritize which destinations to include. Italy brims with historical landmarks, world-class art, and mouthwatering cuisine, yet visiting without breaking the bank requires meticulous planning.

Rome, the eternal city, beckons with its ancient ruins and awe-inspiring Vatican treasures. A frugal approach involves staying in lesser-known neighborhoods such as Testaccio or Trastevere where accommodations are cheaper. Savor Rome’s iconic sights like the Colosseum by purchasing a combined ticket that also grants access to the Roman Forum and Palatine Hill, providing value for money. Furthermore, many of Rome’s wonders—the Pantheon, Trevi Fountain—are free to admire.

Next on our thrifty trail is Florence, cradle of the Renaissance. Florence's compact size makes it ideal for exploration by foot—saving on transportation costs. Admission fees for renowned museums like the Uffizi Gallery can be pricey; however, visiting lesser-known gems such as the Bargello Museum or enjoying panoramic views from Piazzale Michelangelo won’t cost a dime.

Venice's romance is undeniable but often comes with high price tags. To avoid overspending in this lagoon city, opt for a vaporetto (water bus) pass rather than expensive gondola rides. Discover hidden corners of Venice by wandering its maze-like alleys or visit during off-peak seasons when accommodation rates plummet.

Further south lies Naples—a gateway to Pompeii and the Amalfi Coast—yet full of underrated attractions itself. Feast upon authentic pizza napoletana at modest eateries while exploring rich cultural sites like Castel dell'Ovo without straining your wallet.

To truly stretch your euros, consider rail passes if traveling between cities; not only do they offer unlimited travel within certain periods but also enable spontaneous detours to less-traveled towns bursting with charm yet devoid of tourist crowds.

Lastly, immerse yourself in local culture: frequent lively markets for fresh produce instead of dining out every meal; seek out free concerts or street performances; join complimentary walking tours (while remembering to tip guides). Embracing these practices not only saves money but also enriches your connection with Italy’s soulful essence.

In summary, touring Italy's top cities and attractions affordably is entirely feasible with strategic choices—from selecting economical accommodations and embracing public transport to targeting free activities and absorbing local customs. With careful planning and an adventurous spirit, you'll discover that Italy’s riches await those eager to experience them without sacrificing financial peace of mind.