Rome

Here's a suggested itinerary for 5 days in Rome that meets all your constraints:

Day 1:

• Start your day with a visit to the Colosseum, one of the most iconic landmarks in Rome. You can purchase tickets online in advance to avoid long lines.
• After exploring the Colosseum, head over to the Roman Forum and Palatine Hill, which are located nearby. These ancient ruins offer a glimpse into the city's rich history.
• In the afternoon, take a stroll through the Monti neighborhood, which is known for its trendy boutiques and cafes. This area is also popular with the LGBT community, so you'll find plenty of welcoming spots to grab a drink or a bite to eat.

Day 2:

• Spend the morning exploring Vatican City, which is home to some of the world's most famous art and architecture. Be sure to visit St. Peter's Basilica and the Sistine Chapel.
• In the afternoon, head over to Trastevere, a charming neighborhood on the west bank of the Tiber River. This area is known for its narrow streets, colorful buildings, and lively nightlife scene.

Day 3:

• Start your day with a visit to the Pantheon, one of the best-preserved ancient buildings in Rome. This impressive structure was built nearly 2,000 years ago and features a stunning dome.
• Afterward, head over to Piazza Navona, a beautiful square that's surrounded by Baroque architecture. This area is also home to many street performers and artists.
• In the evening, check out the Gay Street area near the Colosseum, which is known for its LGBT-friendly bars and clubs.

Day 4:

• Spend the morning exploring the Appian Way, an ancient road that dates back to the Roman Republic. This area is now a park and offers a peaceful escape from the hustle and bustle of the city.
• In the afternoon, head over to the Testaccio neighborhood, which is known for its food scene. This area is also home to many LGBT-friendly bars and clubs.

Day 5:

• Start your day with a visit to the Trevi Fountain, one of Rome's most famous landmarks. Legend has it that if you throw a coin into the fountain, you'll return to Rome someday.
• Afterward, head over to the Spanish Steps, another popular tourist spot. This area is also home to many high-end shops and boutiques.
• In the evening, check out the LGBT-friendly bars and clubs in the San Lorenzo neighborhood, which is known for its vibrant nightlife scene.

Overall, this itinerary should give you a good mix of history, culture, and nightlife while staying within your budget. Enjoy your trip to Rome!