We can preview Salesforce Lightning Web Component locally without saving/deploying the changes to the server.

Steps:

1. Run the following command to update your Salesforce CLI version to the latest. This step helps in avoiding so many issues, errors and exceptions.

sf update

2. Run the following command to install the Local Dev plugin.

sf plugins install @salesforce/plugin-lightning-dev
(OR)
sf plugins install @salesforce/plugin-lightning-dev@latest

3. Toggle on “Enable Local Dev” in your Salesforce Setup.

4. Run the following command to preview.

sf lightning dev app

5. Make changes to your Salesforce Lightning Web Component. Just save locally and you should be able to see the changes in your preview without deploying it to the server. This saves a lot of time.

Salesforce Article:

https://developer.salesforce.com/docs/platform/lwc/guide/get-started-test-components.html