Available options:

1) Use Avatax Integration:  Avatax is provided by Avalara.  While their website does not explicitly state any pricing, they do have pricing plans for small businesses.  I understand that these pricing plans are based on transaction volume.  This option is most reliable for automatic sales tax calculation in Odoo.

2) Manual Sales Tax Determination: If your transaction volume is less than 50 per month or your sales tax liability is less than USD 1000 per month, and you do not have a sales tax nexus outside your state, then you may be better off manually managing your sales tax determination in Odoo.  This option is least expensive in terms of recurring subscription costs.

3) Custom Development and/or Third Party Odoo Apps:  If you have in-house capabilities to maintain Odoo custom developments and/or third party Odoo Apps, then this is a possibility.  However, this will need your Odoo database to be hosted on Odoo sh or on-premise.  Using custom developments and/or third party Odoo Apps may seem an attractive proposition, but it can create a mess in the future.  This option is the least reliable option, with unpredictable maintenance costs.

Solution I have opted for my small business: I have an online store for selling made-to-order, handcrafted spice blends.  We have used Option 2 until now, however, will likely move to Option 1 sometime later this year.

For the specific point on defining customer-specific tax rates in one of the comments:

Fiscal Positions (Accounting -> Configuration-> Fiscal Positions) allow defining customer-specific sales tax rates, overriding the default sales tax rate defined for the Product.  Being a standard feature of Odoo, this works for all hosting types of Odoo.

For example:

The default sales tax for your state for a product is "Sales Tax 6%".  This will be assigned in the Customer Taxes field for the Product.

Now you may define a Fiscal Position which replaces "Sales Tax 6%" with let's say "Sales Tax 7.25%".  Assign this fiscal position to a customer under the tab "Sales & Purchase" in the section Fiscal Information.  With this setup "Sales Tax 6%" will be substituted automatically by "Sales Tax 7.25%" when creating a quotation/sales order/invoice for this customer.

Tips:

1. It is possible to assign the fiscal position for each individual delivery contact or a billing contact.  This is convenient depending on if you need sales tax calculation based on the shipping address or the billing address.
2. One Fiscal Position allows substitutions of multiple tax rates at product level.  This is convenient if you have multiple tax jurisdictions with different rates for a product category.  You can define all substitutions in the same place by creating a Fiscal Position for each tax jurisdiction and then assign those Fiscal Positions =to respective customers.
3. Fiscal Position also allows the substitution of GL accounts on the product.  This is convenient if your local accounting regulations require a specific tax amount to be posted to a different GL account.
4. The "Detect Automatically" flag in the Fiscal Position definition is not very useful in the context of U.S. domestic taxation.  This flag enables automatic assignment of fiscal positions to customers based on their country or country group.
5. Ensure that the "Use API" checkbox is turned off.

Did you ever get a solution?  I have the same Q... Seems they used to work with taxcloud but that is being cut out now.