Besides gold what are other elements natural or man made that would last forever?

Asking what elements can last forever is a rare example because, with few exception, all elements can last forever. Those exceptions are elements without a stable isotope (found in the source section).

And gold isn't always more expensive than platinum. Machined platinum is much more expensive than gold because platinum is so hard. However, when gold and platinum are in their raw states, gold is much more expensive because it is decently rare and not always in a useable form. Gold also has many more uses than platinum, such as medicine, food and drink, manufacturing, and electronics, among others.

natural elements: I would guess diamond, quartz, tungsten (The chemical element with the highest melting point)...

man made: plastic

As for the price of gold and platinum...

Well, the less of something there is, and the harder it is to obtain, the more it will be worth. Gold follows these principles, as it is not always easily mined and comes at a high price for mining and processing, at least in comparison with other metals.

Gold is also extremely valuable for a number of practical reasons – it is a very malleable substance that can be heated as well as pounded into new shapes. It is so durable that it can sustain its integrity even when pounded so thin it becomes known as “gold leaf,” which is then used for decoration and for gilding.

@ the answerer below,

An atom and an element are NOT the same thing. An element is a much more general term than atom. An atom refers to the smallest particle which still retains the same properties of the element. An atom is just a atom, but Elements are made up of atoms of that element.

Gold and most of the platinum metals, ie Platinum, Palladium, Rhodium, Ruthenium, Osmium, Iridium,

The "price" of Gold is tied to an intrinsic feature of tradition. It is recognized as a tradeable commodity with value as currency, where as the platinum group has largely industry values, and is much more difficult to come by in a pure form and more difficult to isolate in a pure form.

All non radioactive elements last forever. An atom is an element. Atoms can not be destroyed other than in a particle accelerator.