It's tricky to pinpoint one single "cheapest and best" place in Bhutan as "best" is subjective and depends on your interests. However, we can break it down by considering budget-friendly options and popular, worthwhile destinations.

For a balance of affordability and must-see sights:

• Paro: While it's the location of the international airport and the famous Tiger's Nest Monastery (Paro Taktsang), which might seem expensive, Paro offers a concentrated dose of Bhutanese highlights. Why it can be relatively budget-friendly: You can find guesthouses and smaller hotels that are more affordable than luxury resorts. Exploring the town, visiting Rinpung Dzong, the National Museum, and the weekend market doesn't have high entry fees. The hike to Tiger's Nest is challenging but free (you only pay for optional pony rides partway). Things to see: Tiger's Nest Monastery, Rinpung Dzong, National Museum of Bhutan, Kyichu Lhakhang (one of the oldest temples), Drukgyel Dzong ruins, Chele La Pass (highest motorable pass with stunning views).
• Thimphu: As the capital city, Thimphu offers a mix of cultural experiences and some budget-friendly options. Why it can be relatively budget-friendly: Similar to Paro, you can find a range of accommodations. Exploring the city's markets, visiting the Memorial Chorten, and the Buddha Dordenma (giant Buddha statue with great views) are relatively inexpensive activities. Things to see: Tashichho Dzong (government secretariat and monastic body), Buddha Dordenma, National Memorial Chorten, Folk Heritage Museum, Textile Museum, Changangkha Lhakhang (one of the oldest temples in Thimphu), weekend market.

Tips for a Cheaper Trip to Bhutan:

• Travel during the off-season: The shoulder seasons (late February-early March and late November) or even the winter (December-February) and summer/monsoon (June-August) can offer lower prices for accommodations and potentially fewer crowds. However, be aware of weather limitations during these times (e.g., potential road closures in winter, rain in summer).
• Consider overland entry (if coming from India): If you are in India, entering Bhutan by road through Phuentsholing, Samtse, or Gelephu can save on flight costs.
• Stay in budget accommodations: Opt for guesthouses, homestays, or budget hotels instead of luxury resorts. These often provide a more authentic experience as well.
• Eat local: Dine at local restaurants and cafes where Bhutanese food is delicious and more affordable than tourist-centric establishments. Try local staples like Ema Datshi (chili cheese stew), Momos (dumplings), and red rice.
• Use local transport: While hiring a private car and driver is common for tourists, using local buses or shared taxis for inter-city travel can significantly cut down transportation costs. Be prepared for potentially longer travel times.
• Focus on free or low-cost activities: Many of Bhutan's attractions, like dzongs (fortresses), monasteries (from the outside), and scenic viewpoints, have minimal or no entry fees. Hiking trails are also a great way to experience the beauty of Bhutan without spending much.
• Travel in a group: If you're traveling with friends or family, you can split the costs of transportation, guides (if required), and accommodation, making the trip more affordable per person.
• Book directly: Try booking your accommodations directly with the hotels or guesthouses, as third-party booking sites may add extra fees.

Places that might be less expensive but still offer unique experiences:

• Phobjikha Valley: Known for its stunning glacial valley and the winter home of black-necked cranes (from late October to mid-February). Accommodation options here might be slightly less expensive than in Paro or Thimphu. The natural beauty and the Crane Information Centre are key attractions.
• Bumthang: Often considered the spiritual heartland of Bhutan, Bumthang has numerous ancient temples and monasteries. While it's further east and might involve more travel, it offers a rich cultural experience and potentially more budget-friendly stays in smaller towns.

In conclusion, while Paro and Thimphu are popular and offer a good mix of attractions, you can make your visit more affordable by choosing budget-friendly options for accommodation and transport, especially during the off-season. Exploring beyond the main tourist hubs to places like Phobjikha and Bumthang might also offer a more budget-conscious yet rewarding experience.