Maybe not what you’re looking for, but I have a portfolio (watch list) set up on MarketWatch. Select each ticker and enter your holdings and it provides a real time snapshot of the daily price action and links to news.
I also track my portfolio in greater detail on a Google spreadsheet. Again, I enter the ticker and share count, and use the import function to pull in real time data from Google Finance and Finviz. I’ve include cost basis, yield, purchase date, performance, and many other things over time.
Obviously my account numbers, brokerage, personal data, or passwords don’t appear anywhere on either of the above.
I trade with Fidelity which has great information but I don’t linger on the site or stay logged on. I’m not sure of any financial site that won’t log you out after a period of inactivity for obvious reasons.
Good luck, let us know what you find.