I would not use a tomcat install but the jetty based example included with solrSolr. You can find it in the solr/example directory. Try running the start.jar with "java -jar start.jar", does it work?
https://cwiki.apache.org/confluence/display/solr/Running+Solr+on+Jetty "Solr comes with an example schema and scripts for running on Jetty, along with a working installation, in the /example directory. It is stripped of all unnecessary features and its config has had some minor tuning so it's optimized for Solr. It is recommended that you use the provided Jetty server for optimal performance. For more information about the Jetty example installation, see the Solr Tutorial and the basic installation instructions"