I'm currently about halfway through Ανάβασις by Ξενοφών.
I think possibly I might have a crack at Herodotus Histories after that.
I found a great source for a bilingual edition of Ανάβασις in Greek and English here (first book of Ανάβασις in table format here). This format given for Ανάβασις is perfect: a table, with one column in Greek and the other in English. Unfortunately most of the other items on that page are not bilingual editions, and the list also doesn't include Ἡρόδοτος.
With Ανάβασις I've been able to download the HTML tables and convert them into Word documents, with 2 columns. Then I've made the right column (English) very very pale grey (on white background), so that I can only look at it when I really need to. This really works for me as I plough through Kyros's shenanigans (he's just died, so it doesn't look too promising currently). For each sentence I can make my little vocab list, in a cell in a table in the file.
I found this site with a bilingual Ἡρόδοτος Ἱστορίαι (Ἡρόδοτου Ἱστορίαι ;). But the format there is not particularly downloadable as things seem to be on separate pages for the two languages. It may be the best there is publicly available, and I can see that it'd be possible to construct similar two-column tables in Word documents. It'd take a bit more time though.
Does anyone know of any other sites? I'd be interested in bilingual Latin-English sites for Latin authors too.