An RGB-to-VGA converter can probably be found at your nearest Amiga dealer. It shouldn't cost too much, 10-15 € perhaps.
Then you can connect a VGA monitor to your Amiga and run Workbench, Word processors, Web browsers etc. in Multiscan: Productivity. If you keep your TV connected to composite-out you will still be able to play games and watch demos that the VGA monitor won't be able to display.
An amiga multisync monitor would probably be pretty expensive if you can find someone who are willing to sell one. They're very rare but admittedly it's by far the best solution.