What is a Hindu's place of worship called?

Hindu's place of worship is called a Mandir, Devalayam, Devasthanam, or a Hindu temple.

It is a place of worship for followers of Hinduism. A characteristic of most temples is the presence of murtis (statues) of the Hindu deity to whom the temple is dedicated. They are usually dedicated to one primary deity, the presiding deity, and other deities associated with the main deity.

However, some temples are dedicated to several deities, and others are dedicated to murtis in an aniconic form. Many temples are in key geographical points, such as a hill top, near waterfalls, caves and rivers.

This is because some believe the Puranas mention that "The gods always play where groves are near rivers, mountains, and springs."

Hindu temples are known by different names around the world, depending on the language. The word mandir or mandiram is used in many languages and is derived from a Sanskrit word, mandira, for 'house' (of a deity by implication).

Temples are known as Mandir, Devasthanam, Kshetralayam, Punyakshetram, or Punyakshetralayam in Telugu, as Deula / Mandira in Oriya, Devastana in Kannada and Mondir in Bengali, as Kshatriya or Jambalaya in Malayalam. Temples are known as kō-ail in Tamil and occasionally, especially in modern formal speech, Aalayam.

Hindu's worship both at home and at temples. In streets and villages there are simple shrines set up and most Hindu homes have a shrine or Puja (prayer room) where they perform ceremonies and worship.

The worship place in Hinduism is any neat clean airy space because Hinduism believes in One God - who is omnipresent. Hindus have been given the freedom to worship God from wherever they like. However Mandirs or Satsang Bhavans are places where community worships are done by different sects and communities.
Hindus worship everywhere. There are temples in every nook and corner of the country - India. Apart from the temples, Hindus would worship trees, rivers, mountains, birds and animals, rock outcrops, which have been worshiped traditionally. The Banyan and Peepal trees (Ficus Bengalensis and Ficus religiosa) are considered very auspicious. Holy Basil is another shrub which is considered very auspicious.

All Hindu homes keep the shrub and worship it in the morning. No Hindu would agree to cut these trees. Similarly, cows are an object of worship because of the various things that they give us.

There are famous places of pilgrimages. Normally they are far from habitation (temples at the mouth of glaciers or at the top of mountains, or in caves in deep jungles, etc). In olden days, visiting them was an ordeal. But people still did it. Similarly, bathing in large rivers on particular days is considered auspicious. That creates the largest religious gathering in India, the Kumbha Festival. Kumbha congregation is held at four places in India, Haridwar, Allahabad, Nasik, and Ujjain. During one year some 70 million attended the festival over the period of one month.