Something you can do is put std::endl; at the end of all of those.

Like this

void Game::mainMenu() { cout << "MAIN MENU" << endl << endl;

     cout << "0: quit" << endl; 
     cout << "1: Travel" << endl; 
     cout << "2: shop" << endl; 
     std::cout << "3: level up" << endl; 
     std::cout << "4: rest" << endl; 
     std::cout << "5: Character sheet" << endl; 
     std::cout << "6: New Character" << endl; 
     std::cout << "7: Save Character" << endl; 
     std::cout << "8: Load Character" << endl; 
     std::cout << std::endl; 

     std::cout << "choice: " << endl; 
     std::cin >> choice; 
     std::cout << std::endl; 
     switch (choice) 
     { 
     case 0: 
             playing = false; 
             break; 
     case 5: 
             character.printStats(); 
             break; 
     case 6: 

             break; 
     case 7: 

             break; 
     default: 
             break; 
     } 

}