Is there a way to query the blockchain locally if I am running a full node?
If you want to query your full node, you should use the JSON-RPC API. Note that by default, you'll only be able to get blocks, and transactions from your own full node wallet. If you want to be able to query any transactions, you have to add txindex=1 to your configuration file. And compared to using blockchain.info, you won't be able to query balances of addresses.