At the time of the revolution, the vast majority of North America was owned by Spain (France having ceded Louisiana - i.e. the land west of the Mississippi - to Spain in 1762). It wasn't free land, so they'd have had to fight Spain for control of the land.

There was a section of the land between New Spain and the British colonies that was specifically reserved for the Native Americans (roughly around what today we'd consider the Great Lakes region down through Alabama and Mississippi), established by the Proclamation of 1763. British citizens (at the time, this included folks like Washington) were forbidden from entering into the Indian reservation. This was done specifically to protect the British colonists from the threat of Indian invasion (recall that the French and Indian War had only just wrapped up), but landowners like Washington loathed the Proclamation for limiting the expansion of their enterprise.

Also, the basis for the Revolution was not "we want our own country." The basis was "we already have our own country, which is now being subjected to despotism." The colonists were rebelling specifically against what they believed were uniquely unfair laws (e.g. the Stamp Act, the quartering of soldiers). This was not happening only in America–the abuses were also being perpetuated in England–but America was being specifically targeted, and the people of England did nothing to help them. The way the colonists wrote about the rebellion was that it was a necessary evil: that they did not want to break off from Britain, but had to, because the laws set in place were being ignored by King George III and his ministers.

This is actually straightforwardly explained in the Declaration of Independence. The majority of the text of the Declaration is listing a long list of "repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States." These injuries include refusing to pass laws, dissolving representative governmental bodies or making it impossible for people to appeal to these bodies, controlling judges, and overall acting as a tyrant. Again, the problem is not "he is not allowing us to have our own country," it is, "We had our own charters/legislative houses/home rule for years, and now it is being deliberately taken away to take away our autonomy."

They explain how the problem is that they are being subjected to a despot who does not follow the law, and how they have tried to follow the law by appealing to the government, but it hasn't worked:

In every stage of these Oppressions We have Petitioned for Redress in the most humble terms: Our repeated Petitions have been answered only by repeated injury.

Then they explain that they've also tried to appeal to the British citizens, and it hasn't worked:

Nor have We been wanting in attentions to our Brittish brethren. We have warned them from time to time of attempts by their legislature to extend an unwarrantable jurisdiction over us. We have reminded them of the circumstances of our emigration and settlement here. We have appealed to their native justice and magnanimity, and we have conjured them by the ties of our common kindred to disavow these usurpations, which, would inevitably interrupt our connections and correspondence. They too have been deaf to the voice of justice and of consanguinity.

So, even if there had been land west of the colonies for the people to escape to, that would defeat the purpose of the rebellion. The plan wasn't to establish a country just for the sake of it–the plan was to maintain the governmental bodies and legal structures that had existed for years and was only just now (in the eyes of the colonists) being taken away due to the machinations of a tyrant.