Hello! It sounds like an exciting trip you're planning to some iconic places in India.

Best Time to Visit:
The ideal time to visit Ayodhya, Varanasi, and Lucknow is from October to March when the weather is pleasant and conducive to sightseeing. The festive season (October-November) brings an added charm to these cities.

Route and Accessibility:
All three cities have excellent connectivity by rail and road. The nearest airport is in Lucknow, from where you can easily reach Ayodhya and Varanasi by rail or road. Varanasi also has its own airport. If you're traveling from outside India, it's best to fly into Delhi or Mumbai and then take a domestic flight or train.

Accommodation and Booking:
All three cities have a range of accommodations to suit different budgets. Hotels can be booked online via numerous platforms. It's advisable to book accommodations well in advance, especially during the festive season.

Clothing and Essentials:
India's climate can be quite diverse, so pack lightweight cotton clothes for the day and warmer clothes for the cooler nights. An umbrella or rain jacket could also be useful during the monsoon season. Don't forget to pack essentials like a good quality sunscreen, insect repellent, and a reusable water bottle.

Health and Safety:
Ensure your routine vaccinations are up to date before travelling. Drinking bottled water and eating thoroughly cooked food will help you avoid most common health issues. Follow the local COVID-19 guidelines and practice good hygiene to further ensure your safety.

Local Etiquette and Respect:
Indians appreciate respectful behavior. When visiting religious places, dress modestly and remove your shoes before entering. Always ask for permission before taking photographs, especially in religious places. Accept and offer things with your right hand as a mark of respect.