What are some non-Indian and non-Middle Eastern Sufi destinations around the world?

Sufi orders are officially banned in Turkey, which isn't to say that they don't exist there, but that they are highly politicised and mostly exist underground. You are unlikely to find them as a tourist.

The modern Mevlevî "whirling dervish" performances are specially designed for tourists; they might be visually authentic but they do not represent a functioning sufi order. The Mevlevî museum in Konya is pleasant enough to visit, but there isn't a whole lot going on there.

One lesser-visited site in Turkey with connections to sufism is the shrine to the mystic Hac? Bekta? Veli in the town of Hac?bekta? in the province of Nev?ehir (close to Cappadocia). This is not a functional sufi lodge, but Turkey's largest religious minority, the Alevis, regard it as a holy site, so it is much more relevant than any of the "touristic sufi" locations in Turkey. I believe they hold performances of some sort there at certain times of year and there is an annual pilgrimage (in December?).

You can also visit sufi shrines in many other countries, but outwardly most are not much different than any other burial places for holy men. For example, there's a large complex for the founder of the Naqshbandi sufi order just outside Bukhara in Uzbekistan. The only place I've ever witnessed an actual sufi devotional ceremony was in Pakistan, but that doesn't fit the criteria you've set out in your question.

You can find Sufis wherever you find Muslims but in little numbers. Most Sufis are in the Middle East, Africa and the Indian subcontinent.

If you want to find large groups outside these areas it will be hard. Anyway, your best shot outside these areas will be Turkey, where a large portion of the Muslim population is made up of Sufis. You can find a lot of tarikatlar (or lodges) where they practice Sufism and as far as I know they are open-minded and will welcome anyone to join them. Furthermore, Sufis have different sects among them and each one is different from the other. For example, the Mevlevi Order are more into music and dancing and body moves while the Naqshbandi and Qadiriyya are more about songs (Hymns) and less music and body moves. I think you would be more interested in Mevlevi.

I would say in Sindh and Hunza (Pakistan). People there live with Sufi concepts and traditions. In the Northern and Southern part of Pakistan,Islam was preached by Sufi masters. while in the middle Pakistan, Punjab (excluding Multan region) the ready-made religion was imported from the Arab world and therefore people mostly practice Arab culture but not spiritual side of Islam (Sufism). In contrast, Northern Pakistan (specially, Hunza) is populated with 90% of Ismailies and there practices are deeply rooted in Sufism Islam as it was brought to the region around 12 century by sufi masters who traveled from Samarkand to Egypt and came back to the Badkhashan - Northern Pakistan to teach the religion (Sufism). Those Sufis thought the Sufism in-terms of local culture but didn't bring anything from outside except Sufim itself.