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Assuming you are looking for a web mapping with hosting managed for you and various sorts of vector query then one option might be CartoDB. It is backed by a postgres/postgis DB and lets you do various sorts of visualization and mapping without having to setup any services yourself. It includes free options for small tables but you might find you are needing the for-pay levels though even those are quite cheap.
If you are willing to set things up yourself of course you could do things a wide variety of ways - such as setting up postgres+postgis and web map server yourself.
If CartoDB's free offering is not enough, you may also install CartoDB on your own servers. It's open source. (You will have to use Amazon ow some other alternative if you want to be on the cloud)
And here's an article comparing fussion tables to CartoDB (the artcle is from CartoDB, so it's a little biased indeed)
you should check out following cloud based slutions.
Qgis Cloud - Publish your own maps directly from the desktop!
It's free to get started and sign up is instant. Publish your first map within minutes.
Amazon Web Services - Amazon EC2 provides an ideal environment for running your ArcGIS Server applications. Amazon EC2 allows you to quickly configure ArcGIS Server through ready to use ArcGIS Server AMIs; scale ArcGIS Server services and applications leveraging Amazon’s Elastic Cloud Computing infrastructure, and integrate with other Amazon features like Amazon Elastic Block Store (EBS) and Cloud Watch.
MapMart Cloud - MapMart Cloud Web Mapping Service has been developed to serve up the most current and highest quality geospatial data available in a fast and easy way to GIS and non-GIS users alike. The data sets include the CORE data with a wide selection of Aerial, Satellite, Digital Elevation Model (DEM), and Topographic maps, plus Premium Data providing the highest resolution Aerial and Satellite data currently available from the major data providers including, DigitalGlobe, GeoEye, Intermap, and Astrium.
GIS Marketplace - The GIS Marketplace makes it easy to instantly deploy the industry's leading GIS applications.
GIS Cloud - GIS in the Cloud unlocks you from your single-user workstations and lets you just focus on using the solutions. No more worrying about IT, infrastructure, hardware, software, patches, etc. Your data and apps are now in the cloud and instantly available from your desktop, tablet or mobile devices. Our goal is to enrich your work-flows with all that the Cloud brings.
Fusion Tables are going to be shut down.
Google Earth Engine can import and visualize data
Jupyter notebooks can visualize GeoJSON format data using the GeoJSON extension. See Visualizing BigQuery Data in a Jupyter Notebook.
BigQuery Geo Viz can only display up to 2000 results on a map so not suitable for your application. See Visualizing BigQuery GIS Data