Watford, near to Junction Station, would certainly work. There are frequent main line trains to Euston operated by London Northwestern in around 20 minutes. The last train usually, i.e. subject to engineering works etc, leaves Euston after midnight.
I'd also endorse Premier Inn over Travelodge.
If they want to stay in London they could explore the offerings of Imperial London Hotels. They're a very long established family business with several establishments, at different price/market points, around Woburn Place/Russel Square. Euston>Woburn Place>Holborn is an easy walk and well served by buses. The 'rack' rates they quote on Bookings.com etc and on their website can be significantly improved by joining their membership per the header on the website:
www.imperialhotels.co.uk/
I stayed at the Bedford on Friday for a little over £100. That was a single but doubles/trebles were only a few quid more. Breakfast (English) was an extra tenner and OK value but there are loads of chain and independent
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London Stay Advice 
London Stay Advice 
