For white Burgundy, you should be able to find a wine from Marc Colin for around your price range. Also, look for wines from Bouchard Pere, Jadot and Drouhin.
But, as others have said, the best values in white Burgundy are from Chablis. I love the wines of Christian Moreau and Moreau-Naudet. The wines of Samuel Billaud have been recommended to me recently (I bought a couple of bottles this week) but I have not tasted them yet.
For California Chardonnay, try Mount Eden. Mount Eden Chardonnay - Five Decades - WINE TALK - WineBerserkers
For reds, I HIGHLY recommend trying wines older than 2022. 2022 wines are certainly the easiest wines to buy, but if you don’t try wines with some age, what is the point of the tasting? Brane Cantenac is an excellent choice, but I might try something other than Lagrange for a less expensive wine. The 2016 Lafon Rochet is excellent at around that price range.
For California reds, how about Domaine Eden Cabernet at your lower level. If you really want a treat to open yourself up to what California Cabernet can taste like for someone with an old-world palate, try Mount Eden Cabernet. Mount Eden Vineyards
2012 Mount Eden Cabernet Sauvignon, Santa Cruz Mountains - WINE TALK - WineBerserkers