Can't connect to localhost:9200

Ok, I was able to track down (and solve) the problem.

I started the elasticsearch service with sudo -u elasticsearch /usr/share/elasticsearch/bin/elasticsearch and received

[2018-11-29T14:54:48,525][WARN ][o.e.b.ElasticsearchUncaughtExceptionHandler] [xxx] uncaught exception in thread [main]
org.elasticsearch.bootstrap.StartupException: java.lang.IllegalArgumentException: node settings must not contain any index level settings
        at org.elasticsearch.bootstrap.Elasticsearch.init(Elasticsearch.java:140) ~[elasticsearch-6.5.1.jar:6.5.1]
        at org.elasticsearch.bootstrap.Elasticsearch.execute(Elasticsearch.java:127) ~[elasticsearch-6.5.1.jar:6.5.1]
        at org.elasticsearch.cli.EnvironmentAwareCommand.execute(EnvironmentAwareCommand.java:86) ~[elasticsearch-6.5.1.jar:6.5.1]
        at org.elasticsearch.cli.Command.mainWithoutErrorHandling(Command.java:124) ~[elasticsearch-cli-6.5.1.jar:6.5.1]
        at org.elasticsearch.cli.Command.main(Command.java:90) ~[elasticsearch-cli-6.5.1.jar:6.5.1]
        at org.elasticsearch.bootstrap.Elasticsearch.main(Elasticsearch.java:93) ~[elasticsearch-6.5.1.jar:6.5.1]
        at org.elasticsearch.bootstrap.Elasticsearch.main(Elasticsearch.java:86) ~[elasticsearch-6.5.1.jar:6.5.1]
Caused by: java.lang.IllegalArgumentException: node settings must not contain any index level settings
        at org.elasticsearch.common.settings.SettingsModule.<init>(SettingsModule.java:142) ~[elasticsearch-6.5.1.jar:6.5.1]
        at org.elasticsearch.node.Node.<init>(Node.java:373) ~[elasticsearch-6.5.1.jar:6.5.1]
        at org.elasticsearch.node.Node.<init>(Node.java:265) ~[elasticsearch-6.5.1.jar:6.5.1]
        at org.elasticsearch.bootstrap.Bootstrap$5.<init>(Bootstrap.java:212) ~[elasticsearch-6.5.1.jar:6.5.1]
        at org.elasticsearch.bootstrap.Bootstrap.setup(Bootstrap.java:212) ~[elasticsearch-6.5.1.jar:6.5.1]
        at org.elasticsearch.bootstrap.Bootstrap.init(Bootstrap.java:333) ~[elasticsearch-6.5.1.jar:6.5.1]
        at org.elasticsearch.bootstrap.Elasticsearch.init(Elasticsearch.java:136) ~[elasticsearch-6.5.1.jar:6.5.1]
        ... 6 more

With this information I was pointed to Node settings must not contain any index level setting and found two index entries in my elasticsearch.yml:

index.number_of_shards: 3
index.number_of_replicas: 2

After commenting out these lines everything seems back to normal.