There's some hosted ElasticSearch solutions. I like ElastiSearch for search personally.
I have not used any of these services though. I just know they are abundant.
That said, I would seriously consider ElasticSearch if you want a little more robustness. I'd look into the features of these services, but ElasticSearch has many plugins that are super helpful. It's a very robust search engine and it may give you some query feature that you need. Or...It could be overly feature rich and make things confusing.
ElasticSearch with Kibana is also very nice. http://www.elasticsearch.org/overview/kibana/ ...and it looks like Compose.io provides it. This can double down as a great metrics tool for you as well depending on what else you index.