greenh, попробуйте так:

location @fallback {
rewrite ^(.*)$ /tunefrisk/$1 break;
proxy_pass http://api.host.com;
proxy_set_header Host 'api.host.com';
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header X-Real-IP $remote_addr;

}