You do have to cross the river, but they have little boats going across all the time that take about 5 minutes, perhaps they go on demand. Once you are on the ohter side you can hop onto a ferry or there is a Skytrain station right there. We stayed at the Oriental last December, right across the river from the Peninsula. The Oriental actually has facilities on both sides - the main hotel is on one side and the spa, cooking school and one of their restaurants is in the other. I think you can take either the Oriental or the Peninsula boats across, although the Peninsula boat goes right to the hotel dock, whereas the Orinetal boat goes a bit further down for guests going to their spa, etc.

I liked the layout along the river of the Oriental better - it has more riverfront "real estate" for its restaurants, terraces etc. than the Peninsula whose property is narrower on the river, but extends further back.

I would say the "must sees" are:
The Grand Palace, Wat Arun, Wat Phra Keo, Wat Po, Jim Thompson's House, taking a canal tour in a longboat, spending some time at a spa getting a Thai massage, taking a lesson at a Thai cooking school and eating!

I think you can easily do Bangkok on your own. The main sights are located in close proximity to the river, and you can take a ferry, or in the case of Jim Thompson's house, take the Skytrain. Maybe others will have tour guide suggestions.

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Leslie